We present new theoretical mechanisms for quantum speedup in the global optimization of nonconvex functions, expanding the scope of quantum advantage beyond traditional tunneling-based explanations. As our main building-block, we demonstrate a rigorous correspondence between the spectral properties of Schrödinger operators and the mixing times of classical Langevin diffusion. This correspondence motivates a mechanism for separation on functions with unique global minimum: while quantum algorithms operate on the original potential, classical diffusions correspond to a Schrödinger operators with a WKB potential having nearly degenerate global minima. We formalize these ideas by proving that a real-space adiabatic quantum algorithm (RsAA) achieves provably polynomial-time optimization for broad families of nonconvex functions. First, for block-separable functions, we show that RsAA maintains polynomial runtime while known off-the-shelf algorithms require exponential time and structure-aware algorithms exhibit arbitrarily large polynomial runtimes. These results leverage novel non-asymptotic results in semiclassical analysis. Second, we use recent advances in the theory of intrinsic hypercontractivity to demonstrate polynomial runtimes for RsAA on appropriately perturbed strongly convex functions that lack global structure, while off-the-shelf algorithms remain exponentially bottlenecked. In contrast to prior works based on quantum tunneling, these separations do not depend on the geometry of barriers between local minima. Our theoretical claims about classical algorithm runtimes are supported by rigorous analysis and comprehensive numerical benchmarking. These findings establish a rigorous theoretical foundation for quantum advantage in continuous optimization and open new research directions connecting quantum algorithms, stochastic processes, and semiclassical analysis.

Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction. It shifts workloads to a classical computer via partial analytic reconstructions of the quantum model, using only a few evaluations. For each probed gate addition to the ansatz, the simultaneous selection and optimization of the data feature and weight parameter is then entirely classical. Integrated into quantum neural network and quantum kernel support vector classifiers, Q-FLAIR shows state-of-the-art benchmark performance. Since resource overhead decouples from feature dimension, we train a quantum model on a real IBM device in only four hours, surpassing 90% accuracy on the full-resolution MNIST dataset (784 features, digits 3 vs 5). Such results were previously unattainable, as the feature dimension prohibitively drives hardware demands for fixed and search costs for adaptive ansätze. By rethinking feature-map learning beyond black-box optimization, this work takes a concrete step toward enabling quantum machine learning for real-world problems and near-term quantum computers.

Evaluating the permanent of a matrix is a fundamental computation that emerges in many domains, including traditional fields like computational complexity theory, graph theory, many-body quantum theory and emerging disciplines like machine learning and quantum computing. While conceptually simple, evaluating the permanent is extremely challenging: no polynomial-time algorithm is available (unless $\textsc{P} = \textsc{NP}$). To the best of our knowledge there is no publicly available software that automatically uses the most efficient algorithm for computing the permanent. In this work we designed, developed, and investigated the performance of our software package which evaluates the permanent of an arbitrary rectangular matrix, supporting three algorithms generally regarded as the fastest while giving the exact solution (the straightforward combinatoric algorithm, the Ryser algorithm, and the Glynn algorithm) and, optionally, automatically switching to the optimal algorithm based on the type and dimensionality of the input matrix. To do this, we developed an extension of the Glynn algorithm to rectangular matrices. Our free and open-source software package is distributed via Github, at this https URL.

Precision sensing and imaging of weak static magnetic fields are crucial for a variety of emerging nanoscale applications. While nitrogen-vacancy (NV) centers in diamond provide exceptional AC magnetic field sensitivity with nanoscale spatial resolution, their sensitivity to static (DC) magnetic fields is fundamentally limited by the short dephasing time (T2*) due to spin-spin interactions. In this work, we present a novel hybrid sensing approach that integrates a soft ferromagnetic microwire with a single near-surface NV center to amplify its response to external static magnetic fields. This hybrid configuration achieves a DC magnetic field sensitivity of 63 nT/sqrt(Hz) for a single NV center - about 500 times greater than conventional inhomogeneous broadening- or T2*-limited magnetometry, with potential for further enhancement. The compact and highly sensitive nature of this sensor opens new opportunities for quantum sensing applications involving the detection of static or slowly varying magnetic fields across diverse scientific and technological domains.

We show that the quantum smooth label cover problem is RE-hard. This contrasts with the quantum unique label cover problem, which can be decided efficiently by Kempe, Regev, and Toner (FOCS'08). Our result aligns with the RE-hardness of the quantum label cover problem, which follows from the celebrated MIP* = RE result of Ji, Natarajan, Vidick, Wright, and Yuen (ACM'21). Additionally, we show that the quantum oracularized smooth label cover problem is also RE-hard. This aligns with the alternative quantum unique games conjecture on the RE-hardness of the quantum oracularized unique label cover problem proposed by Mousavi and Spirig (ITCS'25). Our techniques employ a series of reductions from the halting problem to the quantum smooth label cover problem, and include a quantum-sound version of Feige's reduction from 3SAT to 3SAT5 (STOC'96), which may be of independent interest.

Electronic voting systems face growing risks from cyberattacks and data breaches, which are expected to intensify with the advent of quantum computing. To address these challenges, we introduce a quantum-secure voting framework that integrates Quantum Key Distribution (QKD), Dual-Key Symmetric Encryption, and verifiable receipt mechanisms to strengthen the privacy, integrity, and reliability of the voting process. The framework enables voters to establish encryption keys securely, cast encrypted ballots, and verify their votes through receipt-based confirmation, all without exposing the vote contents. To evaluate performance, we simulate both quantum and classical communication channels using the Message Queuing Telemetry Transport (MQTT) protocol. Results demonstrate that the system can process large numbers of votes efficiently with low latency and minimal error rates. This approach offers a scalable and practical path toward secure, transparent, and verifiable electronic voting in the quantum era.

Quantum data hiding is the existence of pairs of bipartite quantum states that are (almost) perfectly distinguishable with global measurements, yet close to indistinguishable when only measurements implementable with local operations and classical communication are allowed. Remarkably, data hiding states can also be chosen to be separable, meaning that secrets can be hidden using no entanglement that are almost irretrievable without entanglement -- this is sometimes called `nonlocality without entanglement'. Essentially two families of data hiding states were known prior to this work: Werner states and random states. Hiding Werner states can be made either separable or globally perfectly orthogonal, but not both -- separability comes at the price of orthogonality being only approximate. Random states can hide many more bits, but they are typically entangled and again only approximately orthogonal. In this paper, we present an explicit construction of novel group-symmetric data hiding states that are simultaneously separable, perfectly orthogonal, and even invariant under partial transpose, thus exhibiting the phenomenon of nonlocality without entanglement to the utmost extent. Our analysis leverages novel applications of numerical analysis tools to study convex optimisation problems in quantum information theory, potentially offering technical insights that extend beyond this work.

Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to encode PDEs into unitary time evolution and has potential for scalable electromagnetic analysis. We formulate Maxwell's equations in the potential representation and embed governing equations, boundary conditions, and observables consistently into Hamiltonian form. A key bottleneck is the exponential growth of Hamiltonian terms for complex geometries; we examine this issue and show that logical compression can substantially mitigate it, especially for periodic or symmetric structures. As a proof of concept, we simulate optical wave propagation through a metalens and illustrate that the method can capture wavefront shaping and focusing behavior, suggesting its applicability to design optimization tasks. This work highlights the feasibility of Hamiltonian-based quantum simulation for photonic systems and identifies structural conditions favorable for efficient execution.

The diamond sensor has emerged as a promising platform for quantum sensing, enabling the estimation of physical quantities -- such as microwave~(MW) field -- with precision unattainable by classical counterpart. However, traditional diamond sensors suffer severe precision degradation when the signal MW is not resonant with the sensor transition frequency. Here, we propose and demonstrate a Floquet diamond sensor~(FDS) for high-precision off-resonant MW amplitude sensing without attenuating the strength of the signal MW. The periodic driven field effectively induces an quasi-energy shift that matches the off-resonant MW frequency. The measurement precision of FDS is characterized by quantum Fisher information, which approaches the ultimate precision -- Heisenberg limit -- within the coherent time. Furthermore, the FDS exhibits robust tolerance to practical control errors and is compatible with dynamical coupling protocol, enabling a robust and high-sensitivity magnetic sensing. Our results confirm the quantum advantage of quantum sensing and provide a practical technology for high-precision off-resonant MW sensing.

Broadband nonlinear optical devices play a critical role in both classical and quantum optics. Here, we design and fabricate a 6.82-mm-long step-chirped periodically poled lithium niobate~(CPPLN) waveguide on lithium niobate on insulator, which enables quasi-phase matching over a broad bandwidth for second-harmonic generation~(SHG) and spontaneous parametric down-conversion~(SPDC). The SHG achieves an average efficiency of 54.4\%/W/cm$^2$ over the first-harmonic wavelength range of 1510~nm-1620~nm, paving the way for realizing SPDC across a wide range of pump wavelengths. For SPDC, by tuning the pump wavelength to 775~nm, 780~nm, and 785~nm, we achieve broadband photon-pair generation with a maximum full bandwidth and brightness up to 99~THz~(846~nm) and 20~GHz/mW/nm, respectively. Our findings provide an efficient and experiment-friendly approach for generating broadband photon pairs, which holds significant promise for advancing applications in quantum metrology.

The polarization-entangled photon source (PEPS) at non-degenerated wavelengths is pivotal to connect quantum systems working at different wavelengths, with the assistance of quantum teleportation. Here, a compact Sagnac-type photon source is designed and demonstrated, in which two photons with wavelengths at 810 and 1550~nm are highly entangled in polarization degree of freedom. The two photons are generated from a periodically poled lithium niobate crystal pumped with a 532~nm continuous-wave laser, via type-0 nondegenerate spontaneous parametric down-conversion. The polarization of three lights is rotated by a single periscope, which makes the Sagnac interferometer compact and stable. The generated two photons are with high brightness of $3\times10^4$ pairs/s/mW, which are highly entangled with fidelity of $0.985\pm0.002$. The entanglement is verified by violating the Clauser-Horne-Shimony-Holt inequality with $\mathcal S =2.756\pm0.007$. Finally, teleportation is demonstrated with this nondegenerate source, in which photonic states at 810~nm is teleported to 1550~nm with fidelity of $0.955\pm0.003$.

Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are transformed by linear maps (superchannels) in order to simulate other gates. To develop a full hierarchy of quantum resources, beyond those first two orders, and to account for the fact that quantum protocols can interconvert resources of different orders, we need a theoretical framework that addresses all orders in a uniform manner. We introduce a framework based on a system of types, which label the different kinds of objects that are present at different orders. We equip the framework with a parallel product operation that modifies and generalizes the tensor product so as to be operationally meaningful for maps of distinct and arbitrary orders. Finally, we introduce a family of convex cones that generalize the notion of complete positivity to all orders, with the aim of characterizing the objects that are physically admissible, facilitating an operational treatment of quantum objects at any order.

We give new evidence that quantum circuits are substantially more powerful than classical circuits. We show, relative to a random oracle, that polynomial-size quantum circuits can sample distributions that subexponential-size classical circuits cannot approximate even to TV distance $1-o(1)$. Prior work of Aaronson and Arkhipov (2011) showed such a separation for the case of exact sampling (i.e. TV distance $0$), but separations for approximate sampling were only known for uniform algorithms. A key ingredient in our proof is a new hardness amplification lemma for the classical query complexity of the Yamakawa-Zhandry (2022) search problem. We show that the probability that any family of query algorithms collectively finds $k$ distinct solutions decays exponentially in $k$.

We propose a quantum-classical hybrid method for solving large-scale mixed-integer quadratic problems (MIQP). Although extended Benders decomposition is effective for MIQP, its master problem which handles the integer and quadratic variables often becomes a computational bottleneck. To address this challenge, we integrate the D-Wave CQM solver into the decomposition framework to solve the master problem directly. Our results show that this hybrid approach efficiently yields near-optimal solutions and, for certain problem instances, achieves exponential speedups over the leading commercial classical solver. These findings highlight a promising computational strategy for tackling complex mixed-integer optimization problems.

Silicon quantum chips offer a promising path toward scalable, fault-tolerant quantum computing, with the potential to host millions of qubits. However, scaling up dense quantum-dot arrays and enabling qubit interconnections through shuttling are hindered by uncontrolled lateral variations of the valley splitting energy $E_{VS}$. We map $E_{VS}$ across a $40 \, $nm x $400 \, $nm region of a $^{28}$Si/Si$_{0.7}$Ge$_{0.3}$ shuttle device and analyze the spin coherence of a single electron spin transported by conveyor-belt shuttling. We observe that the $E_{VS}$ varies over a wide range from $1.5 \, \mu$eV to $200 \, \mu$eV and is dominated by SiGe alloy disorder. In regions of low $E_{VS}$ and at spin-valley resonances, spin coherence is reduced and its dependence on shuttle velocity matches predictions. Rapid and frequent traversal of low-$E_{VS}$ regions induces a regime of enhanced spin coherence explained by motional narrowing. By selecting shuttle trajectories that avoid problematic areas on the $E_{VS}$ map, we achieve transport over tens of microns with coherence limited only by the coupling to a static electron spin entangled with the mobile qubit. Our results provide experimental confirmation of the theory of spin-decoherence of mobile electron spin-qubits and present practical strategies to integrate conveyor-mode qubit shuttling into silicon quantum chips.

We propose a novel method for enhancing phase estimation in the displacement-assisted SU(1,1) (DSU(1,1)) interferometer by incorporating the photon recycling technique, evaluated under single-intensity detection (SID) and homodyne detection (HD) schemes. Our analysis showed that utilizing the photon recycling technique, the photon-recycled DSU(1,1) interferometer performs better than the conventional DSU(1,1) interferometer for some conditions. We also showed that this improvement is possible in both SID and HD schemes. In addition, to discuss the maximum sensitivity achieved by our proposed model, we have calculated the quantum Cramér-Rao bound (QCRB) within the framework and found that our proposed model approaches the QCRB. Therefore, we believe that our findings offer a promising new approach to improve phase sensitivity through photon recycling.

A quantum computing algorithm for rhythm generation is presented, which aims to expand and explore quantum computing applications in the arts, particularly in music. The algorithm maps quantum random walk trajectories onto a rhythmspace -- a 2D interface that interpolates rhythmic patterns. The methodology consists of three stages. The first stage involves designing quantum computing algorithms and establishing a mapping between the qubit space and the rhythmspace. To minimize circuit depth, a decomposition of a 2D quantum random walk into two 1D quantum random walks is applied. The second stage focuses on biasing the directionality of quantum random walks by introducing classical potential fields, adjusting the probability distribution of the wave function based on the position gradient within these fields. Four potential fields are implemented: a null potential, a linear field, a Gaussian potential, and a Gaussian potential under inertial dynamics. The third stage addresses the sonification of these paths by generating MIDI drum pattern messages and transmitting them to a Digital Audio Workstation (DAW). This work builds upon existing literature that applies quantum computing to simpler qubit spaces with a few positions, extending the formalism to a 2D x-y plane. It serves as a proof of concept for scalable quantum computing-based generative random walk algorithms in music and audio applications. Furthermore, the approach is applicable to generic multidimensional sound spaces, as the algorithms are not strictly constrained to rhythm generation and can be adapted to different musical structures.

Entanglement witnessing is essential for quantum technologies such as computing, key distribution, and networking. Conventional bulk-optics methods require sequential reconfiguration across multiple polarization bases, limiting efficiency and scalability. We propose a metasurface-based analyzer that performs dual-basis (\sigma_z and \sigma_y) projections simultaneously by mapping them to orthogonal spatial modes. This allows direct access to the commuting two-photon correlators \langle \sigma_z \otimes \sigma_z \rangle and \langle \sigma_y \otimes \sigma_y \rangle required for entanglement witnessing. The metasurface design employs meta-atoms engineered to impart independent linear and circular phase delays through anisotropy and geometric control, resulting in polarization-dependent beam deflection that separates H/V and R/L components. This approach halves the measurement overhead compared to sequential analysis while offering a compact, integrable platform for chip-scale quantum photonics. The proposed scheme provides a path toward efficient entanglement verification with applications in quantum key distribution, quantum repeaters, and scalable quantum networks.

Laser-driven operations are a common approach for engineering one- and two-qubit gates in trapped-ion arrays. Measuring key parameters of these lasers, such as beam sizes, intensities, and polarizations, is central to predicting and optimizing gate speeds and stability. Unfortunately, it is challenging to accurately measure these properties at the ion location within an ultra-high vacuum chamber. Here, we demonstrate how the ions themselves may be used as sensors to directly characterize the laser beams needed for quantum gate operations. Making use of the four-photon Stark Shift effect in $^{171}$Yb$^+$ ions, we measure the profiles, alignments, and polarizations of the lasers driving counter-propagating Raman transitions. We then show that optimizing the parameters of each laser individually leads to higher-speed Raman-driven gates with smaller susceptibility to errors. Our approach demonstrates the capability of trapped ions to probe their local environments and to provide useful feedback for improving system performance.

Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum signal processing (QSP), whose circuit depth is proportional to the degree of the polynomial. Previous studies exploit the Chebyshev polynomial approximation, which requires a Chebyshev series of degree $O(\sqrt{n\ln(1/\delta)})$ for an $n$-degree polynomial, where $\delta$ is the approximation error. However, the approximation is limited to only a few functions, including monomials, truncated exponential, Gaussian, and error functions. In this work, we present the most generalized function approximation methods for $\delta$-approximating linear combinations or products of polynomial-approximable functions with quadratically reduced-degree polynomials. We extend the list of polynomial-approximable functions by showing that the functions of cosine and sine can also be $\delta$-approximated by quadratically reduced-degree Laurent polynomials. We demonstrate that various Hamiltonian functions for quantum ground-state preparation and energy estimation can be implemented with quadratically shallow circuits.

We consider a quasi-PT-symmetric system of two resonators, one of which interacts with a finite-size environment. The interaction with the environment leads to energy losses in the resonators, and the finite size of the environment leads to a non-Markovian dynamics of the relaxation process. We demonstrate that non-Markovian processes in the quasi-PT-symmetric system can make the states of the system infinitely living, loss-protected states, even in the absence of gain. There is a critical value of the interaction between the resonator and the environment below which any state of the system is loss-protected. When the interaction magnitude is greater than the critical value, depending on the coupling strength between the resonators, either one or both states are unprotected. We show that the boundaries of regions with different numbers of protected states are determined by the relaxation rates in the quasi-PT-symmetric system, calculated in the Markovian approximation. By changing the coupling strength between the resonators and the interaction magnitude between the resonator and the environment, the system switches between modes with two, one, or no loss-protected states. This makes it possible to realize stable PT-symmetric devices based on purely dissipative systems. The obtained results are applicable to quantum systems with single excitations, allowing the concept of PT symmetry to be extended to such systems.

We examine the stationary--state equations for lattices with generalized Markovian dephasing and relaxation. When the Hamiltonian is quadratic, the single--particle correlation matrix has a closed system of equations even in the presence of these two processes. The resulting equations have a vectorized form related to, but distinct from, Lyapunov's equation. We present an efficient solution that helps to achieve the scaling limit, e.g., of the current decay with lattice length. As an example, we study the super--diffusive--to--diffusive transition in a lattice with long--range hopping and dephasing. The approach enables calculations with up to $10^4$ sites, representing an increase of $10$ to $40$ times over prior studies. This enables a more precise extraction of the diffusion exponent, enhances agreement with theoretical results, and supports the presence of a phase transition. There is a wide range of problems that have Markovian relaxation, noise, and driving. They include quantum networks for machine--learning--based classification and extended reservoir approaches (ERAs) for transport. The results here will be useful for these classes of problems.

With the rapid advances in quantum computer architectures and the emerging prospect of large-scale quantum memory, it is becoming essential to classically verify that remote devices genuinely allocate the promised quantum memory with specified number of qubits and coherence time. In this paper, we introduce a new concept, proofs of quantum memory (PoQM). A PoQM is an interactive protocol between a classical probabilistic polynomial-time (PPT) verifier and a quantum polynomial-time (QPT) prover over a classical channel where the verifier can verify that the prover has possessed a quantum memory with a certain number of qubits during a specified period of time. PoQM generalize the notion of proofs of quantumness (PoQ) [Brakerski, Christiano, Mahadev, Vazirani, and Vidick, JACM 2021]. Our main contributions are a formal definition of PoQM and its constructions based on hardness of LWE. Specifically, we give two constructions of PoQM. The first is of a four-round and has negligible soundness error under subexponential-hardness of LWE. The second is of a polynomial-round and has inverse-polynomial soundness error under polynomial-hardness of LWE. As a lowerbound of PoQM, we also show that PoQM imply one-way puzzles. Moreover, a certain restricted version of PoQM implies quantum computation classical communication (QCCC) key exchange.

Recent advances in combining Clifford circuits with tensor network (TN) states have shown that classically simulable disentanglers can significantly reduce entanglement, mitigating the bond-dimension bottleneck in TN simulations. In this work, we develop a variational TN framework based on Grassmann tensor networks, which natively encode fermionic statistics while preserving locality. By incorporating locally defined Clifford circuits within the fermionic formalism, we simulate benchmark models including the tight-binding and $t$-$V$ models. Our results show that Clifford disentangling removes the classically simulable component of entanglement, leading to a reduced bond dimension and improved accuracy in ground-state energy estimates. Interestingly, imposing the natural Grassmann-evenness constraint on the Clifford circuits significantly reduces the number of disentangling gates, from 720 to just 32, yielding a far more efficient implementation. These findings highlight the potential of Clifford-augmented Grassmann TNs as a scalable and accurate tool for studying strongly correlated fermionic systems, particularly in higher dimensions.

We discuss recent advances in applying Quantum Information Science to problems in high-energy nuclear physics. After outlining key developments, open challenges, and emerging connections between these disciplines, we highlight recent results on the study of matter states, hard probes, and spin correlations using novel quantum technologies. This work summarizes the corresponding presentation delivered at the Quark Matter 2025 conference in Frankfurt, Germany.

Bosonic codes, leveraging infinite-dimensional Hilbert spaces for redundancy, offer great potential for encoding quantum information. However, the realization of a practical continuous-variable bosonic code that can simultaneously correct both single-photon loss and dephasing errors remains elusive, primarily due to the absence of exactly orthogonal codewords and the lack of an experiment-friendly state preparation scheme. Here, we propose a code based on the superposition of squeezed Fock states with an error-correcting capability that scales as $\propto\exp(-7r)$, where $r$ is the squeezing level. The codewords remain orthogonal at all squeezing levels. The Pauli-X operator acts as a rotation in phase space is an error-transparent gate, preventing correctable errors from propagating outside the code space during logical operations. In particular, this code achieves high-precision error correction for both single-photon loss and dephasing, even at moderate squeezing levels. Building on this code, we develop quantum error correction schemes that exceed the break-even threshold, supported by analytical derivations of all necessary quantum gates. Our code offers a competitive alternative to previous encodings for quantum computation using continuous bosonic qubits.

We employ the operational quasiprobability (OQ) as a work distribution, which reproduces the Jarzynski equality and yields the average work consistent with the classical definition. The OQ distribution can be experimentally implemented through the end-point measurement and the two-point measurement scheme. Using this framework, we demonstrate the explicit contribution of coherence to the fluctuation, the average, and the second moment of work. In a two-level system, we show that non-joint measurability, a generalized notion of measurement incompatibility, can increase the amount of extractable work beyond the classical bound imposed by jointly measurable measurements. We further prove that the real part of Kirkwood-Dirac quasiprobability (KDQ) and the OQ are equivalent in two-level systems, and they are nonnegative for binary unbiased measurements if and only if the measurements are jointly measurable. In a three-level Nitrogen-vacancy center system, the OQ and the KDQ exhibit different amounts of negativities while enabling the same work extraction, implying that the magnitude of negativity is not a faithful indicator of nonclassical work. These results highlight that coherence and non-joint measurability play fundamental roles in the enhancement of work.

We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to the steady state follows a power law, reflecting the interplay between Hamiltonian dynamics and vanishing dissipation. The decay exponents vary non-analytically with the ramp rate, exhibiting a cusp singularity, and $n$-point correlation functions factorize into one- and two-point contributions. Our exact solution anchors a universality class of open quantum systems with explicitly time-dependent dissipation.

Higher symmetries in interacting many-body systems often give rise to new phases and unexpected dynamical behavior. Here, we theoretically investigate a variant of the Dicke model with higher-order discrete symmetry, resulting from complex-valued coupling coefficients between quantum emitters and a bosonic mode. We propose a driven-dissipative realization of this model focusing on optomechanical response of a driven atom tweezer array comprised of $n$ sub-ensembles and placed within an optical cavity, with the phase of the driving field advancing stepwise between sub-ensembles. Examining stationary points and their dynamical stability, we identify a phase diagram for $n\geq 3$ with three distinctive features: a $\mathbb{Z}_n$ ($\mathbb{Z}_{2n}$) symmetry-breaking superradiant phase for even (odd) $n$, a normal unbroken-symmetry phase that is dynamically unstable due to non-reciprocal forces between emitters, and a first-order phase transition separating these phases. This $n$-phase Dicke model may be equivalently realized in a variety of optomechanical or opto-magnonic settings, where it can serve as a testbed for studying high-order symmetry breaking and non-reciprocal interactions in open systems.

A special class of states of 2-qubits which are simultaneously separable and have positive semidefinite Wigner functions is described.

Accurate state preparation is a critical bottleneck in many quantum algorithms, particularly those for ground state energy estimation. Even in fault-tolerant quantum computing, preparing a quantum state with sufficient overlap to the desired eigenstate remains a major challenge. To address this, we develop a unified framework for filtered-state preparation that enhances the overlap of a given input state through spectral filtering. This framework encompasses the polynomial and trigonometric realizations of filters, allowing a transparent analysis of the trade-offs between overlap amplification and preparation cost. As examples, we introduce signal-processing-inspired filters, such as Gaussian filters and Krylov subspace-based filters, that adaptively suppress excited-state contributions using low-rank projections. Within this framework, we further develop a filtered variant of QPE (FQPE) that mitigates the unfavorable dependence on the initial overlap present in standard QPE. Numerical experiments on Fermi-Hubbard models show that FQPE reduces the total runtime by more than two orders of magnitude in the high-precision regime, with overlap amplification exceeding a factor of one hundred.

Silicon nitride microresonators driven by strong pump pulses can generate squeezed light in a dominant spectral-temporal mode, a central resource for continuous-variable quantum computation. In the high parametric gain regime, several effects, including self- and cross-phase modulation as well as time-ordering corrections, become significant and can degrade source performance. In this work, we comprehensively investigate the generation of squeezed light from a silicon nitride resonator under pulsed pumping, spanning from low to high parametric gain up to 16 photons/pulse. We experimentally study how the average photon number and the first- and second- order correlations of the squeezed marginal modes evolve with increasing pulse energy, across various frequency detunings and pulse durations. Furthermore, we analyze the errors introduced by multi-pair emissions in estimating the joint temporal intensity via time-resolved coincidence measurements. We propose and demonstrate an error-correction strategy based on the marginal distributions of time-resolved multi-photon events. Our results provide a practical strategy for optimizing the gain and the temporal mode structure of pulsed squeezed light sources in microresonators, elucidating the physical mechanisms and limitations that govern source performance in the high gain regime.

The ability to precisely control and predict the evolution of quantum states is a fundamental requirement for advancing quantum technologies. Here, we develop tunable atomic routing protocols based on an integrable model of dipolar bosons confined in a four-well potential with a star-shaped configuration. By adjusting the system parameters, we identify a harmonic dynamical regime of the atomic population that can be treated analytically, providing a complete description of the system's behaviour for precise manipulation. We demonstrate three independent modes of control over the atomic population dynamics under the action of an external field: frequency tuning via variation in the field intensity, directional switching via spatial displacement of the field, and amplitude modulation by varying its duration. These modes operate under two distinct configurations: one source and two drains, and, in reverse order, two sources and one drain. These cases emulate an atomic 1:2 demultiplexer and 2:1 multiplexer, respectively. Our results may contribute to the development of control mechanisms in the design of quantum devices.

Parallelization is a major challenge in quantum algorithms due to physical constraints like no-cloning. This is vividly illustrated by the conjecture of Moore and Nilsson from their seminal work on quantum circuit complexity [MN01, announced 1998]: unitaries of a deceptively simple form--controlled-unitary "staircases"--require circuits of minimum depth $\Omega(n)$. If true, this lower bound would represent a major break from classical parallelism and prove a quantum-native analogue of the famous NC $\neq$ P conjecture. In this work we settle the Moore-Nilsson conjecture in the negative by compressing all circuits in the class to depth $O(\log n)$, which is the best possible. The parallelizations are exact, ancilla-free, and can be computed in poly($n$) time. We also consider circuits restricted to 2D connectivity, for which we derive compressions of optimal depth $O(\sqrt{n})$. More generally, we make progress on the project of quantum parallelization by introducing a quantum blockwise precomputation technique somewhat analogous to the method of Arlazarov, Dinič, Kronrod, and Faradžev [Arl+70] in classical dynamic programming, often called the "Four-Russians method." We apply this technique to more-general "cascade" circuits as well, obtaining for example polynomial depth reductions for staircases of controlled $\log(n)$-qubit unitaries.

Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its range of applications further. In this article, we propose a novel application of this advanced quantum walk search algorithm for the edge detection of images\textemdash a critical task in digital image processing. Given the probabilistic nature of quantum computing, obtaining measurement result with a high success probability is essential alongside faster computation time. Our quantum walk search algorithm demonstrates a high success probability in detecting the image edges compared to the existing quantum edge detection methods and outperforms classical edge detection methods with a quadratically faster speed. A small Qiskit circuit implementation of our method using a one-dimensional quantum walk search has been executed in Qiskit's $qasm\_simulator$ and $ibm\_sydney(fake)$ device.

The discrete-time quantum walk on the Johnson graph $J(n,k)$ is a useful tool for performing target vertex searches with high success probability. This graph is defined by $n$ distinct elements, with vertices being all the \(\binom{n}{k}\) $k$-element subsets and two vertices are connected by an edge if they differ exactly by one element. However, most works in the literature focus solely on the search for a single target vertex on the Johnson graph. In this article, we utilize lackadaisical quantum walk--a form of discrete-time coined quantum walk with a wighted self-loop at each vertex of the graph--along with our recently proposed modified coin operator, $\mathcal{C}_g$, to find multiple target vertices on the Johnson graph $J(n,k)$ for various values of $k$. Additionally, a comparison based on the numerical analysis of the performance of the $\mathcal{C}_g$ coin operator in searching for multiple target vertices on the Johnson graph, against various other frequently used coin operators by the discrete-time quantum walk search algorithms, shows that only $\mathcal{C}_g$ coin can search for multiple target vertices with a very high success probability in all the scenarios discussed in this article, outperforming other widely used coin operators in the literature.

Few-body physics explores quantum systems of a small number of particles, bridging the gap between single-particle and many-body regimes. To provide an accessible tool for such studies, we present this http URL, a Julia package for quantum few-body simulations. The package supports general two- and three-body systems in various spatial dimensions with arbitrary pair-interactions, and allows to calculate bound and resonant states. The implementation is based on the well-established Gaussian expansion method and we illustrate the package's capabilities through benchmarks and research examples. The package comes with documentation and examples, making it useful for research, teaching, benchmarking, and method development.

One-way puzzles (OWPuzzs) introduced by Khurana and Tomer [STOC 2024] are a natural quantum analogue of one-way functions (OWFs), and one of the most fundamental primitives in ''Microcrypt'' where OWFs do not exist but quantum cryptography is possible. OWPuzzs are implied by almost all quantum cryptographic primitives, and imply several important applications such as non-interactive commitments and multi-party computations. A significant goal in the field of quantum cryptography is to base OWPuzzs on plausible assumptions that will not imply OWFs. In this paper, we base OWPuzzs on hardness of non-collapsing measurements. To that end, we introduce a new complexity class, $\mathbf{SampPDQP}$, which is a sampling version of the decision class $\mathbf{PDQP}$ introduced in [Aaronson, Bouland, Fitzsimons, and Lee, ITCS 2016]. We show that if $\mathbf{SampPDQP}$ is hard on average for quantum polynomial time, then OWPuzzs exist. $\mathbf{SampPDQP}$ is the class of sampling problems that can be solved by a classical polynomial-time algorithm that can make a single query to a non-collapsing measurement oracle, which is a ''magical'' oracle that can sample measurement results on quantum states without collapsing the states. Such non-collapsing measurements are highly unphysical operations that should be hard to realize in quantum polynomial-time. We also study upperbounds of the hardness of $\mathbf{SampPDQP}$. We introduce a new primitive, distributional collision-resistant puzzles (dCRPuzzs), which are a natural quantum analogue of distributional collision-resistant hashing [Dubrov and Ishai, STOC 2006]. We show that dCRPuzzs imply average-case hardness of $\mathbf{SampPDQP}$ (and therefore OWPuzzs as well). We also show that two-message honest-statistically-hiding commitments with classical communication and one-shot signatures [Amos, Georgiou, Kiayias, Zhandry, STOC 2020] imply dCRPuzzs.

Meyer and Wallach proposed the average norm squared of the wedge products of the projections of a state onto the single qubit subspaces as the global entanglement measure. Meyer and Wallach's global entanglement has the significant impact. We propose the average determinant of reduced density matrices for each qubit as a global entanglement measure. We show that these two measures are the same algebraically though they use different concepts. By means of the properties of reduced density matrices, we can explore the present measure. We propose a decomposition law for the present measure, demonstrate that the present measure just measures the average mixedness for each qubit and the average 1-tangle, and indicate that for n-qubit W state, the average mixedness for each qubit and 1-tangle almost vanish for large number of qubits. We also point out that for two quits, the present measure is just the square of the concurrence while for three qubits, the present measure is or greater than 3-tangle.

Approximate quantum error correction (AQEC) provides a versatile framework for both quantum information processing and probing many-body entanglement. We reveal a fundamental tension between the error-correcting power of an AQEC and the hardness of code state preparation. More precisely, through a novel application of the Lovász local lemma, we establish a fundamental trade-off between local indistinguishability and circuit complexity, showing that orthogonal short-range entangled states must be distinguishable via a local operator. These results offer a powerful tool for exploring quantum circuit complexity across diverse settings. As applications, we derive stronger constraints on the complexity of AQEC codes with transversal logical gates and establish strong complexity lower bounds for W state preparation. Our framework also provides a novel perspective for systems with Lieb-Schultz-Mattis type constraints.

Scalable quantum computation demands high-fidelity two-qubit gates. However, decoherence and control errors are inevitable, which can decrease the quality of implemented quantum operations. We propose a robust iSWAP gate protocol for semiconductor spin qubits, which is a promising platform for scalable quantum computing. Our scheme uses only local microwave drives on conventional exchange-coupled spin qubits. This approach simultaneously addresses two critical challenges on semiconductor quantum computing: it suppresses low-frequency noise via continuous dynamical decoupling, and it circumvents the control difficulties associated with the ac modulation of the exchange interaction. We further develop a composite pulse sequence to remove drive-strength constraints and a dynamically corrected method to provide first-order immunity to microwave amplitude this http URL simulations confirm that our scheme can achieve fidelity above the fault-tolerance threshold under current experimental conditions, offering a building block for practical quantum processors.

Pseudorandom functions (PRFs) are one of the most fundamental primitives in classical cryptography. On the other hand, in quantum cryptography, it is possible that PRFs do not exist but their quantum analogues could exist, and still enabling many applications including SKE, MACs, commitments, multiparty computations, and more. Pseudorandom unitaries (PRUs) [Ji, Liu, Song, Crypto 2018], pseudorandom isometries (PRIs) [Ananth, Gulati, Kaleoglu, Lin, Eurocrypt 2024], and pseudorandom function-like state generators (PRFSGs) [Ananth, Qian, Yuen, Crypto 2022] are major quantum analogs of PRFs. PRUs imply PRIs, and PRIs imply PRFSGs, but the converse implications remain unknown. An important open question is whether these natural quantum analogues of PRFs are equivalent. In this paper, we partially resolve this question by ruling out black-box constructions of them: 1. There are no black-box constructions of $O(\log\lambda)$-ancilla PRUs from PRFSGs. 2. There are no black-box constructions of $O(\log\lambda)$-ancilla PRIs with $O(\log\lambda)$ stretch from PRFSGs. 3. There are no black-box constructions of $O(\log\lambda)$-ancilla PRIs with $O(\log\lambda)$ stretch from PRIs with $\Omega(\lambda)$ stretch. Here, $O(\log\lambda)$-ancilla means that the generation algorithm uses at most $O(\log\lambda)$ ancilla qubits. PRIs with $s(\lambda)$ stretch is PRIs mapping $\lambda$ qubits to $\lambda+s(\lambda)$ qubits. To rule out the above black-box constructions, we construct a unitary oracle that separates them. For the separations, we construct an adversary based on the quantum singular value transformation, which would be independent of interest and should be useful for other oracle separations in quantum cryptography.

As of now, an optimal quantum algorithm solving partial differential equations eludes us. There are several different methods, each with their own strengths and weaknesses. In past years comparisons of these existing methods have been made, but new work has emerged since then. Therefore, we conducted a survey on quantum methods developed post-2020, applying two such solvers to the heat equation in one spatial dimension. By analyzing their performance (including the cost of classical extraction), we explore their precision and runtime efficiency advancements between the two, identifying advantages and considerations.

Recently, bicycle-sharing systems have been implemented in numerous cities, becoming integral to daily life. However, a prevalent issue arises when intensive commuting demand leads to bicycle shortages in specific areas and at particular times. To address this challenge, we employ a novel quantum machine learning model that analyzes time series data by fitting quantum time evolution to observed sequences. This model enables us to capture actual trends in bicycle counts at individual ports and identify correlations between different ports. Utilizing the trained model, we simulate the impact of proactively adding bicycles to high-demand ports on the overall rental number across the system. Given that the core of this method lies in a Monte Carlo simulation, it is anticipated to have a wide range of industrial applications.

Isospectrally patterned lattices (IPL) have recently been shown to exhibit a rich band structure comprising both regimes of localized as well as extended states. The localized states show a single center localization behaviour with a characteristic localization length. We derive a continuum analogue of the IPL which allows us to determine analytically its eigenvalue spectrum and eigenstates thereby obtaining an expression for the localization length which involves the ratio of the coupling among the cells of the lattice and the phase gradient across the lattice. This continuum model breaks chiral symmetry but still shows a pairing of partner states with positive and negative energies except for the ground state. We perform a corresponding symmetry analysis which illuminates the continuum models structure as compared to a corresponding chirally symmetric Hamiltonian.

Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We introduce a scheme for performing generalized surgery on quantum LDPC codes using a constant number of rounds of syndrome measurement. The merged code in our scheme is constructed by taking the total complex of the base code and a suitably chosen homomorphic chain complex. We demonstrate the applicability of our scheme on an example multi-cycle code and assess the performance under a phenomenological noise model, showing that fast surgery performs comparably to standard generalized surgery with multiple rounds. Our results pave the way towards fault-tolerant quantum computing with LDPC codes with both low spatial and temporal overheads.

Quantum error-correcting codes (QECCs) require high encoding rate in addition to high threshold unless a sufficiently large number of physical qubits are available. The many-hypercube (MHC) codes defined as the concatenation of the [[6,4,2]] quantum error-detecting code have been proposed as high-performance and high-encoding-rate QECCs. However, the concatenated codes have a disadvantage that the syndrome weight grows exponentially with respect to the concatenation level. To address this issue, here we propose subsystem quantum codes based on the MHC codes. In particular, we study the smallest subsystem MHC codes, namely, subsystem codes derived from the concatenated [[4,2,2]] error-detecting codes. The resulting codes have a constant syndrome-measurement weight of 4, while keeping high encoding rates. We develop the block-MAP and neural-network decoders and show that they demonstrate superior performance to the bounded-distance decoder.

We investigate superadditivity of quantum capacity through private channels whose Choi-Jamiolkowski operators are private states. This perspective links the security structure of private states to quantum capacity and clarifies the role of the shield system: information encoded in the shield system that would otherwise leak to the environment can be recycled when paired with an assisting channel, thereby boosting capacity. Our main contributions are threefold: Firstly, we develop a general framework that provides a sufficient condition for capacity amplification, which is formulated in terms of the assisting channel's Holevo information. As examples, we give explicit, dimension and parameter dependent amplification thresholds for erasure and depolarizing channels. Secondly, assuming the Spin alignment conjecture, we derive a single-letter expression for the quantum capacity of a family of private channels that are neither degradable, anti-degradable, nor PPT; as an application, we construct channels with vanishing quantum capacity yet unbounded private capacity. Thirdly, we further analyze approximate private channels: we give an alternative proof of superactivation that extends its validity to a broader parameter regime, and, by combining amplification bounds with continuity estimates, we establish a metric separation showing that channels exhibiting capacity amplification have nonzero diamond distance from the set of anti-degradable channels, indicating that existing approximate (anti-)degradability bounds are not tight. We also revisit the computability of the regularized quantum capacity and modestly suggest that this fundamental question still remains open.

High-speed generation and efficient entanglement detection on a photonic chip are essential for quantum information applications but hard to achieve due to common photonic chips' material properties and limited component performance. In this work, we experimentally demonstrate entanglement witness on a silicon photonic chip, with multi-rail single-photon entanglement generation based on decoy-state techniques. The detection is based on balanced homodyne detectors on the same photonic chip with a bandwidth of up to 12.5 GHz, which allows room-temperature operation. A loss-equivalent analysis method compensates for optical losses and system noises. Experimental results quantify an entangled state fidelity of 92% in quantum state tomography and a Clauser-Horne-Shimony-Holt (CHSH) violation lower bound of 2.59. These results establish a viable path toward fully integrated, high-bandwidth, room-temperature quantum photonic systems, with potential applications in on-chip quantum optics and quantum random number generation.

Three-qubit gates are highly beneficial operations in quantum computing, enabling compact implementations of quantum algorithms and efficient generation of multipartite entangled states. However, realizing such gates with high fidelity remains challenging due to crosstalk, complex control requirements, and the overhead of parametric or tunable couplers. In this work, we propose and analyze the implementation of fast, high-fidelity three-qubit gates using giant atoms--artificial atoms coupled to a waveguide at multiple spatially separated points. By leveraging interference effects intrinsic to the giant-atom architecture, we demonstrate that native three-qubit gates, such as the controlled-CZ-SWAP (CCZS) and the dual-iSWAP (DIV), can be realized through simple frequency tuning, without the need for complex pulse shaping or additional hardware. We evaluate gate performance under realistic decoherence and show that fidelities exceeding 99.5% are achievable with current experimental parameters in superconducting circuits. As an application, we present a scalable protocol for preparing three- and five-qubit GHZ states using minimal gate depth, achieving high state fidelity within sub-300ns timescales. Our results position giant-atom systems as a promising platform for entangled-state preparation and low-depth quantum circuit design in near-term quantum computers and quantum simulators.

We revisit the quantum reverse Shannon theorem, a central result in quantum information theory that characterizes the resources needed to simulate quantum channels when entanglement is freely available. We derive a universal additive upper bound on the smoothed max-information in terms of the sandwiched Rényi mutual information. This bound yields tighter single-shot results, eliminates the need for the post-selection technique, and leads to a conceptually simpler proof of the quantum reverse Shannon theorem. By consolidating and streamlining earlier approaches, our result provides a clearer and more direct understanding of the resource costs of simulating quantum channels.

Fault-tolerance using constant space-overhead against long-range correlated errors is an important practical question. In the pioneering works [Terhal and Burkard, PRA 2005], [Aliferis et al, PRA 2005], [Aharonov et al, PRL 2006], fault-tolerance using poly-logarithmic overhead against long-range correlation modeled by pairwise joint Hamiltonian was proven when the total correlation of an error at a qubit location with errors at other locations was $O(1)$, i.e., the total correlation at a location did not scale with the number of qubits. This condition, under spatial symmetry, can simply be stated as the correlation between locations decaying faster than $\frac{1}{\text{dist}^{\text{dim}}}$. However, the pairwise Hamiltonian model remained intractable for constant overhead codes. Recently, [Bagewadi and Chatterjee, PRA 2025] introduced and analyzed the generalized hidden Markov random field (MRF) model, which provably captures all stationary distributions, including long-range correlations [Kunsch et al, Ann. App. Prob. 1995]. It resulted in a noise threshold in the case of long-range correlation, for memory corrected by the linear-distance Tanner codes [Leverrier and Zemor, FOCS 2022] for super-polynomial time. In this paper, we prove a similar result for square-root distance qLDPC codes and provide an explicit expression for the noise threshold in terms of the code rate, for up to $o(\sqrt{\text{\#qubits}})$ scaling of the total correlation of error at a location with errors at other locations.

Quantum annealing provides a practical realization of adiabatic quantum computation and has emerged as a promising approach for solving large-scale combinatorial optimization problems. However, current devices remain constrained by sparse hardware connectivity, which requires embedding logical variables into chains of physical qubits. This embedding overhead limits scalability and reduces reliability as longer chains are more prone to noise-induced errors. In this work, building on the known structural result that the average chain length in clique embeddings grows linearly with the problem size, we develop a mathematical framework that connects embedding-induced overhead with hardware noise in D-Wave's Zephyr topology. Our analysis derives closed-form expressions for chain break probability and chain break fraction under a Gaussian control error model, establishing how noise scales with embedding size and how chain strength should be adjusted with chain length to maintain reliability. Experimental results from the Zephyr topology-based quantum processing unit confirm the accuracy of these predictions, demonstrating both the validity of the theoretical noise model and the practical relevance of the derived scaling rule. Beyond validating a theoretical model against hardware data, our findings establish a general embedding-aware noise framework that explains the trade-off between chain stability and logical coupler fidelity. Our framework advances the understanding of noise amplification in current devices and provides quantitative guidance for embedding-aware parameter tuning strategies.

Multipartite entanglement has much more complex structures than bipartite entanglement, such as the semiseparable state. The multipartite state absent of multipartite entanglement is called a 2-producible state, which is a tensor product of at most 2-partite states. Recently, it is proved that a tripartite pure state is 2-producible if and only if the gap between entanglement of purification and its lower bound vanishes. Here, we show that the entanglement of purification gap is not sufficient to detect more than tripartite entanglement with 4-partite random stabilizer states. We then generalize entanglement of purification to the multipartite case, where the gap between generalized entanglement of purification and its lower bound quantifies the quantum communication cost for distributing one part of the multipartite system to the other parts. We also demonstrate that a multipartite state is 2-producible if and only if the generalized entanglement of purification gaps vanish. In addition, we show that the generalized entanglement of purification gaps are related to the local recoverability of the multipartite state from its marginal state on some parts of the system and the distance between the state and the 2-producible states with the relative entropy. Moreover, we calculate the generalized entanglement of purification gaps for the states fulfilling the generalized Schmidt decomposition, which implies that the 4-partite stabilizer states do not always have the generalized Schmidt decomposition. Our results provide a quantitive characterization of multipartite entanglement in multipartite system, which will promote further investigations and understanding of multipartite entanglement.

We present novel, exotic types of frame changes for the calculation of quantum evolution operators. We detail in particular the biframe, in which a physical system's evolution is seen in an equal mixture of two different standard frames at once. We prove that, in the biframe, convergence of all series expansions of the solution is quadratically faster than in `conventional' frames. That is, if in laboratory frame or after a standard frame change the error at order $n$ of some perturbative series expansion of the evolution operator is on the order of $\epsilon^n$, $0<\epsilon<1$, for a computational cost $C(n)$ then it is on the order of $\epsilon^{2n+1}$ in the biframe for the same computational cost. We demonstrate that biframe is one of an infinite family of novel frames, some of which lead to higher accelerations but require more computations to set up initially, leading to a trade-off between acceleration and computational burden.

This thesis focuses on the Lie-theoretic foundations of controlled open quantum systems. We describe Markovian open quantum system evolutions by Lie semigroups, whose corresponding infinitesimal generators lie in a special type of convex cone - a Lie wedge. The Lie wedge associated to a given control system therefore consists of all generators of the quantum dynamical semigroup that are physically realisable as a result of the interplay between the coherent and incoherent processes the quantum system is subject to. For $n$-qubit open quantum systems, we provide a parametrisation of the largest physically relevant Lie algebra (the system algebra), in which these Lie wedges are contained: the Lindblad-Kossakowski Lie algebra. This parametrisation provides several useful benefits. First, it allows us to construct explicit forms of these system Lie wedges and their respective system Lie algebras. Second, we analyse which control scenarios yield Lie wedges that are closed under Baker-Campbell-Hausdorff (BCH) multiplication and therefore generate Markovian semigroups of time-independent quantum channels. Lie wedges of this form are called Lie semialgebras, and we completely solve this open problem by proving that Lie wedges specialise to this form only when the coherent controls have no effect on both the inherent drift Hamiltonian and the incoherent part of the dynamics. Finally, this parametrisation of the Lindblad-Kossakowski Lie algebra points to an intuitive separation between unital and non-unital dissipative dynamics, where the non-unital component of the dynamics is described by affine translation operations. These translation operators are then exploited to construct purely dissipative fixed-point engineering schemes to obtain either pure or mixed states as a system's unique fixed point.

Quantum entanglement and squeezing associated with the motions of massive mechanical oscillators play an essential role in both fundamental science and emerging quantum technologies, yet realizing such macroscopic nonclassical states remains a formidable challenge. In this paper, we investigate how to achieve strong optomechanical entanglement and mechanical squeezing in a membrane-embedded cavity optomechanical system incorporating a coherent feedback loop, where the membrane interacts with the cavity mode through both linear and quadratic optomechanical couplings. This hybrid optomechanical architecture offers a flexible tunability of intrinsic system parameters, thus allowing the membrane to be stiffened or softened through tuning the sign of quadratic optomechanical coupling and the cavity decay rate to be reduced via feedback control. Exploiting these unique features, we demonstrate that optomechanical entanglement can be substantially enhanced with positive coupling sign and suitable feedback parameters, while strong mechanical squeezing beyond the 3dB limit is simultaneously achieved over a broad parameter range with negative coupling sign, reaching squeezing degree above 10dB under optimized conditions. Our proposal, establishing an all-optical method for generating highly entangled or squeezed states in cavity optomechanical systems, opens up a new route to explore macroscopic quantum effects and to advance quantum information processing.

Conditional Value-at-Risk (CVaR) is a leading tail-risk measure in finance, central to both regulatory and portfolio optimization frameworks. Classical estimation of CVaR and its gradients relies on Monte Carlo simulation, incurring $O(1/\epsilon^2)$ sample complexity to achieve $\epsilon$-accuracy. In this work, we design and analyze a quantum subgradient oracle for CVaR minimization based on amplitude estimation. Via a tripartite proposition, we show that CVaR subgradients can be estimated with $O(1/\epsilon)$ quantum queries, even when the Value-at-Risk (VaR) threshold itself must be estimated. We further quantify the propagation of estimation error from the VaR stage to CVaR gradients and derive convergence rates of stochastic projected subgradient descent using this oracle. Our analysis establishes a near-quadratic improvement in query complexity over classical Monte Carlo. Numerical experiments with simulated quantum circuits confirm the theoretical rates and illustrate robustness to threshold estimation noise. This constitutes the first rigorous complexity analysis of quantum subgradient methods for tail-risk minimization.

In this paper, we define and benchmark a hybrid quantum-classical machine learning pipeline by performing a binary classification task applied to a real-world financial use case. Specifically, we implement a Quantum Reservoir Computing (QRC) layer within a classical routine that includes data preprocessing and binary classification. The reservoir layer has been executed on QuEra's Aquila, a 256-qubit neutral atom simulator, using two different types of encoding: position and local detuning. In the former case, classical data are encoded into the relative distance between atoms; in the latter, into pulse amplitudes. The developed pipeline is applied to predict credit card defaults using a public dataset and a wide variety of traditional classifiers. The results are compared with a fully-classical pipeline including a Deep Neural Network (DNN) model. Additionally, the impact of hardware noise on classification performance is evaluated by comparing the results obtained using Aquila within the classification workflow with those obtained using a classical, noiseless emulation of the quantum system. The results indicate that the noiseless emulation achieves competitive performance with the fully-classical pipeline, while noise significantly degrades overall performance. Although the results for this specific use case are comparable to those of the classical benchmark, the flexibility and scalability of QRC highlight strong potential for a wide range of applications.

Secure key leasing (SKL) enables the holder of a secret key for a cryptographic function to temporarily lease the key using quantum information. Later, the recipient can produce a deletion certificate, which proves that they no longer have access to the secret key. The security guarantee ensures that even a malicious recipient cannot continue to evaluate the function, after producing a valid deletion certificate. Most prior work considers an adversarial recipient that obtains a single leased key, which is insufficient for many applications. In the more realistic collusion-resistant setting, security must hold even when polynomially many keys are leased (and subsequently deleted). However, achieving collusion-resistant SKL from standard assumptions remains poorly understood, especially for functionalities beyond decryption. We improve upon this situation by introducing new pathways for constructing collusion-resistant SKL. Our main contributions are as follows: - A generalization of quantum-secure collusion-resistant traitor tracing called multi-level traitor tracing (MLTT), and a compiler that transforms an MLTT scheme for a primitive X into a collusion-resistant SKL scheme for primitive X. - The first bounded collusion-resistant SKL scheme for PRFs, assuming LWE. - A compiler that upgrades any single-key secure SKL scheme for digital signatures into one with unbounded collusion-resistance, assuming OWFs. - A compiler that upgrades collusion-resistant SKL schemes with classical certificates to ones having verification-query resilience, assuming OWFs.

We extend the scheme of neutral atom Rydberg $C_Z$ gate based on double sequence of adiabatic pulses applied symmetrically to both atoms using counterdiabatic driving in the regime of Rydberg blockade. This provides substantial reducing of quantum gate operation times (at least five times) compared to previously proposed adiabatic schemes, which is important for high-fidelity entanglement due to finite Rydberg lifetimes. We analyzed schemes of adiabatic rapid passage with counterdiabatic driving for single-photon, two-photon and three-photon schemes of Rydberg excitation for rubidium and cesium atoms. We designed laser pulse profiles with fully analytical shapes and calculated the Bell fidelity taking into account atomic lifetimes and finite blockade strengths. We show that the upper limit of the Bell fidelity reaches ${\mathcal F}\simeq0.9999$ in a room-temperature environment.

Noncommutativity of observables is a central feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the laws of thermodynamics for systems with noncommuting, that is, non-Abelian, conserved quantities. We here derive nonequilibrium generalizations of the second law of thermodynamics in the form of fluctuation relations, both for mechanically and thermally driven quantum systems. We identify a non-Abelian contribution to the energy and entropy balances, without which these relations would be violated. The latter term can be controlled to enhance both work extraction and nonequilibrium currents compared to what is obtained in commuting thermodynamics. These findings demonstrate that noncommutativity maybe a useful thermodynamic resource.

We consider the problem of imaging two partially coherent sources and derive the ultimate quantum limits for estimating all relevant parameters, namely their separation, relative intensity, as well as their coherence factor. We show that the separation of the two sources can be super-resolved over the entire range of all other pertinent parameters (with the exception of fully coherent sources), with anti-correlated sources furnishing the largest possible gain in estimation precision, using a binary spatial mode demultiplexing measurement positioned at the center of intensity of the joint point spread function for the two sources. In the sub-Rayleigh limit, we show that both the relative intensity, as well as the real part of the coherence factor, can be optimally estimated by a simple boson counting measurement, making it possible to optimally estimate the separation, relative intensity and real coherence factor of the sources simultaneously. Within the same limit, we show that the imaging problem can be effectively reduced to one where all relevant parameters are encoded in the Bloch vector of a two-dimensional system. Using such a model we find that indirect estimation schemes, which attempt to extract estimates of the separation of the two sources by measuring the purity of the corresponding state of the two-level system, yield suboptimal estimation precision for all non-zero values of the coherence factor.

The thermodynamic uncertainty relation quantifies a trade-off between the relative fluctuations of trajectory currents and the thermodynamic cost, indicating that the current precision is fundamentally constrained by entropy production. In classical bipartite systems, it has been shown that information flow between subsystems can enhance the current precision alongside thermodynamic dissipation. In this study, we investigate how information flow, local dissipation, and quantum effects jointly constrain current fluctuations within a subsystem of interacting quantum systems. Unlike classical bipartite systems, quantum subsystems can exhibit simultaneous state changes and maintain quantum coherence, which fundamentally alters the precision-dissipation trade-off. For this general setting, we derive a quantum thermokinetic uncertainty relation for interacting multipartite systems, establishing a thermodynamic trade-off between current fluctuations, information flow, local dissipation, and quantum effects. Our analysis shows that, in addition to local dissipation, both information exchange and quantum coherence play essential roles in suppressing current fluctuations. These results have important implications for the performance of quantum thermal machines, such as information-thermodynamic engines and quantum clocks. We validate our theoretical findings through numerical simulations on two representative models: an autonomous quantum Maxwell's demon and a quantum clock. These results extend uncertainty relations to multipartite open quantum systems and elucidate the functional role of information flow in fluctuation suppression.

In this paper we extend the applicability of Fox-Wright functions beyond mathematics, specifically in quantum physics. We focused our attention on a new application, on the connection between the Fox-Wright functions and the generalized coherent states formalism. We constructed the generalized coherent states in the Barut-Girardello manner, in which the Fox-Wright functions play the role of normalization functions, and we demonstrated that the Fox-Wright coherent states satisfy all general conditions imposed on the set of coherent states. In parallel, we examined the properties of both pure and mixed (thermal) Fox-Wright coherent states. All calculations were performed within the diagonal operators ordering technique (DOOT) using the Dirac's bra-ket formalism. Finally, we introduced some (specifically, integral) feedback elements that Fox-Wright coherent states induce in the theory of special functions, including a new integral representation of Fox-Wright functions.

A qubit, or quantum bit, is conventionally defined as "a physical system for storing information that is capable of existing in either of two quantum states or in a superposition of both". In this paper, we examine the simple question of whether two distinct levels, each consisting of multiply degenerate sub-states, could serve as a practical quantum bit. We explore this idea using a well-characterized atomic system of the kind employed in several quantum computing implementations. We approximate the atom as a two-level system without degeneracy lifting in the magnetic quantum number while using the angular momentum addition rules to select the desired state transition. We find that, in the continuous presence of the field, the atom still undergoes Rabi oscillations, which are suitable for quantum gate construction. In addition, we compute the average fidelity in quantum gate performance for a single degenerate atom and postulate the required form of two-atom interaction to construct a controlled Z gate.

The commutative depth model allows gates that commute with each other to be performed in parallel. We show how to compute Clifford operations in constant commutative depth more efficiently than was previously known. Bravyi, Maslov, and Nam [Phys. Rev. Lett. 129:230501, 2022] showed that every element of the Clifford group (on $n$ qubits) can be computed in commutative depth 23 and size $O(n^2)$. We show that the Prefix Sum problem can be computed in commutative depth 16 and size $O(n \log n)$, improving on the previous depth 18 and size $O(n^2)$ bounds. We also show that, for arbitrary Cliffords, the commutative depth bound can be reduced to 16. Finally, we show some lower bounds: that there exist Cliffords whose commutative depth is at least 4; and that there exist Cliffords for which any constant commutative depth circuit has size $\Omega(n^2)$.

We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inverse of the allowable error. This transform, which maps basis states to states whose amplitudes are proportional to the Hermite functions, can be interpreted as the Gaussian analogue of the Fourier transform. Our algorithm is based on a method to exponentially fast forward the evolution of the quantum harmonic oscillator, which significantly improves over prior art. We apply this Hermite transform to give examples of provable quantum query advantage in property testing and learning. In particular, we show how to efficiently test the property of being close to a low- degree in the Hermite basis when inputs are sampled from the Gaussian distribution, and how to solve a Gaussian analogue of the Goldreich-Levin learning task efficiently. We also comment on other potential uses of this transform to simulating time dynamics of quantum systems in the continuum.

We show that it is undecidable to determine whether the commuting operator value of a nonlocal game is strictly greater than 1/2. As a corollary, there is a boolean constraint system (BCS) game for which the value of the Navascués-Pironio-Acín (NPA) hierarchy does not attain the commuting operator value at any finite level. Our contribution involves establishing a computable mapping from Turing machines to BCS nonlocal games in which the halting property of the machine is encoded as a decision problem for the commuting operator value of the game. Our techniques are algebraic and distinct from those used to establish MIP*=RE.

In this work, we develop new pulse designs and embedding strategies to improve the analog quantum subroutines of hybrid column generation (CG) algorithms based on neutral-atoms quantum computers (NAQCs). These strategies are designed to improve the quality and diversity of the samples generated. We apply these to an important combinatorial optimization (CO) problem in logistics, namely the fleet assignment. Depending on the instance tested, our quantum protocol has a performance that is either comparable or worse than the best classical method tested, both in terms of the number of iterations and final objective value. We identify the cause of these suboptimal solutions as a result of our quantum protocol often generating high-quality but degenerate samples. We address this limitation by introducing a greedy post-processing technique, Make\_Diff, which applies bit-wise modifications to degenerate samples in order to return a non-degenerate set. With this modification, our quantum protocol becomes competitive with an exact solver for the subproblem, all the while being resilient to state preparation and measurements (SPAM) errors. We also compare our CG scheme with a Gurobi solver and find that it performs better on over 50\% of our synthetic instances and that, despite Gurobi having a more extensive runtime. These improvements and benchmarks herald the potential of deploying hybrid CG schemes on NISQ devices for industrially relevant CO problems.

Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-relevant tasks. Recent advances in algorithmic, detailed-balance Lindbladians enable the efficient simulation of open-system dynamics converging towards desired target states. However, the overall complexity of such schemes is governed by system-size dependent mixing times. In this work, we analyse algorithmic Lindbladians for Gibbs state preparation and prove that they exhibit rapid mixing, i.e., convergence in time poly-logarithmic in the system size. We first establish this for non-interacting spin systems, free fermions, and free bosons, and then show that these rapid mixing results are stable under perturbations, covering weakly interacting qudits and perturbed non-hopping fermions. Our results constitute the first efficient mixing bounds for non-commuting qudit models and bosonic systems at arbitrary temperatures. Compared to prior spectral-gap-based results for fermions, we achieve exponentially faster mixing, further featuring explicit constants on the maximal allowed interaction strength. This not only improves the overall polynomial runtime for quantum Gibbs state preparation, but also enhances robustness against noise. Our analysis relies on oscillator norm techniques from mathematical physics, where we introduce tailored variants adapted to specific Lindbladians $\unicode{x2014}$ an innovation that we expect to significantly broaden the scope of these methods.

We pose and solve the problem of quantum filtering based on continuous-in-time quadrature measurements (homodyning) for the case where the quantum process is in a thermal state. The standard construction of quantum filters involves the determination of the conditional expectation onto the von Neumann algebra generated by the measured observables with the non-demolition principle telling us to restrict the domain (the observables to be estimated) to the commutant of the algebra. The finite-temperature case, however, has additional structure: we use the Araki-Woods representation for the measured quadratures, but the Tomita-Takesaki theory tells us that there exists a separate, commuting representation and therefore the commutant will have a richer structure than encountered in the Fock vacuum case. We apply this to the question of quantum trajectories to the Davies-Fulling-Unruh model. Here, the two representations are interpreted as the fields in the right and left Rindler wedges.

In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The input and output to the quantum algorithm is represented by a set of boundary vertices, and the hyperedges act like switches, connecting the input vertex to the output that the algorithm computes. Apart from generalizing the graph composition framework, our new proposed framework unifies the quantum divide and conquer framework, the decision-tree framework, and the unified quantum walk search framework. For the decision trees, we additionally construct a quantum algorithm from an improved weighting scheme in the non-boolean case. For quantum walk search, we show how our techniques naturally allow for amortization of the subroutines' costs. Previous work showed how one can speed up ``detection'' of marked vertices by amortizing the costs of the quantum walk. In this work, we extend these results to the setting of ``finding'' such marked vertices, albeit in some restricted settings. Along the way, we provide a novel analysis of irreducible, reversible Markov processes, by linear-algebraically connecting its effective resistance to the random walk operator. This significantly simplifies the algorithmic implementation of the quantum walk search algorithm, achieves an amortization speed-up for quantum walks over Johnson graphs, avoids the need for quantum fast-forwarding, and removes the log-factors from the query complexity statements.

Quantum cryptographic definitions are often sensitive to the number of copies of the cryptographic states revealed to an adversary. Making definitional changes to the number of copies accessible to an adversary can drastically affect various aspects including the computational hardness, feasibility, and applicability of the resulting cryptographic scheme. This phenomenon appears in many places in quantum cryptography, including quantum pseudorandomness and unclonable cryptography. To address this, we present a generic approach to boost single-copy security to multi-copy security and apply this approach to many settings. As a consequence, we obtain the following new results: -One-copy stretch pseudorandom state generators (under mild assumptions) imply the existence of t-copy stretch pseudorandom state generators, for any fixed polynomial t. -One-query pseudorandom unitaries with short keys (under mild assumptions) imply the existence of t-query pseudorandom unitaries with short keys, for any fixed polynomial t. -Assuming indistinguishability obfuscation and other standard cryptographic assumptions, there exist identical-copy secure unclonable primitives such as public-key quantum money and quantum copy-protection.

The Clifford hierarchy is a fundamental structure in quantum computation whose mathematical properties are not fully understood. In this work, we characterize permutation gates -- unitaries which permute the $2^n$ basis states -- in the third level of the hierarchy. We prove that any permutation gate in the third level must be a product of Toffoli gates in what we define as \emph{staircase form}, up to left and right multiplications by Clifford permutations. We then present necessary and sufficient conditions for a staircase form permutation gate to be in the third level of the Clifford hierarchy. As a corollary, we construct a family of non-semi-Clifford permutation gates $\{U_k\}_{k\geq 3}$ in staircase form such that each $U_k$ is in the third level but its inverse is not in the $k$-th level.

Classical error-correcting codes are powerful but incompatible with quantum noise, which includes both bit-flips and phase-flips. We introduce Hadamard-based Virtual Error Correction (H-VEC), a protocol that empowers any classical bit-flip code to correct arbitrary Pauli noise with the addition of only a single ancilla qubit and two layers of controlled-Hadamard gates. Through classical post-processing, H-VEC virtually filters the error channel, projecting the noise into pure Y-type errors that are subsequently corrected using the classical code's native decoding algorithm. We demonstrate this by applying H-VEC to the classical repetition code. Under a code-capacity noise model, the resulting protocol not only provides full quantum protection but also achieves an exponentially stronger error suppression (in distance) than the original classical code, and even larger improvements over the surface code while using much fewer qubits, simpler checks and straight-forward decoding. H-VEC comes with a sampling overhead due to its post-processing nature. It represents a new hybrid quantum error correction and mitigation framework that redefines the trade-offs between physical hardware requirements and classical processing for error suppression.

Quantum state transfer (QST) via homogeneous spin chains plays a crucial role in building scalable quantum hardware. A basic quantum state transmission protocol prepares a state in one qubit and transfers it to another through a channel, seeking to minimize the time and avoid information loss. The fidelity of the process is measured by functions proportional to the transition probability between both states. We approach this optimization problem using constant magnetic pulses and two complementary strategies: deep reinforcement learning, where an agent learns pulse sequences through rewards, and genetic algorithms, which develop candidate solutions through selection and mutation. We analyze the efficiency of both methods and their ability to incorporate physical constraints.

One of the most fundamental problems in the field of hypothesis testing is the identity testing problem: whether samples from some unknown distribution $\mathcal{G}$ are actually from some explicit distribution $\mathcal{D}$. It is known that when the distribution $\mathcal{D}$ has support $[N]$, the optimal sample complexity for the identity testing problem is roughly $O(\sqrt{N})$. However, many distributions of interest, including those which can be sampled efficiently, have exponential support size, and therefore the optimal identity tester also requires exponential samples. In this paper, we bypass this lower bound by considering restricted settings. The above $O(\sqrt{N})$ sample complexity identity tester is constructed so that it is not fooled by any (even inefficiently-sampled) distributions. However, in most applications, the distributions under consideration are efficiently sampleable, and therefore it is enough to consider only identity testers that are not fooled by efficiently-sampled distributions. In that case, we can focus on efficient verification with efficient identity testers. We investigate relations between efficient verifications of classical/quantum distributions and classical/quantum cryptography, and show the following results: (i) Every quantumly samplable distribution is verifiable with a $\mathbf{P^{PP}}$ algorithm. (ii) If one-way functions exist, then no sufficiently random classically samplable distribution is efficiently verifiable. (iii) If one-way functions do not exist, then every classically samplable distribution is efficiently verifiable. (iv) If QEFID pairs exist, then there exists a quantumly samplable distribution which is not efficiently verifiable. (v) If one-way puzzles do not exist, then it is possible to verify sampling-based quantum advantage with a efficient quantum computer.

We investigate quantum analogues of collision resistance and obtain separations between quantum ``one-way'' and ``collision-resistant'' primitives. 1. Our first result studies one-wayness versus collision-resistance defined over quantum circuits that output classical strings. We show that there is a classical oracle $\mathcal{O}$ relative to which (sub-exponentially secure) indistinguishability obfuscation and one-way permutations exist even against adversaries that make quantum queries to a non-collapsing measurement oracle, $\mathcal{Q}^{\mathcal{O}}$. Very roughly, $\mathcal{Q}^{\mathcal{O}}$ outputs the result of multiple non-collapsing measurements on the output of any quantum $\mathcal{O}$-aided circuit. This rules out fully black-box {\em quantum} constructions of $Y$ from $X$ for any $X \in \{$indistinguishability obfuscation and one-way permutations, public-key encryption, deniable encryption, oblivious transfer, non-interactive ZK, trapdoor permutations, quantum money$\}, Y \in \{$collision-resistant hash functions, hard problems in SZK, homomorphic encryption, distributional collision-resistant puzzles$\}$. 2. Our second result studies one-wayness versus collision-resistance defined over quantum states. Here, we show that relative to the same classical oracle $\mathcal{O}$, (sub-exponentially secure) indistinguishability obfuscation and one-way permutations exist even against adversaries that make quantum queries to a {\em cloning unitary} $\mathsf{QCol}^\mathcal{O}$. Very roughly, this latter oracle implements a well-defined, linear operation to clone a subset of the qubits output by any quantum $\mathcal{O}$-aided circuit. This rules out fully black-box constructions of quantum lightning from public-key quantum money.

The asymmetry between heating and cooling in open quantum systems is a hallmark of nonequilibrium dynamics, yet its thermodynamic origin has remained unclear. Here, we investigate the thermalization of a quantum system weakly coupled to a thermal bath, focusing on the entropy production rate and the quantum thermokinetic uncertainty relation (TKUR). We derive an analytical expression for the entropy production rate, showing that heating begins with a higher entropy production, which drives faster thermalization than cooling. The quantum TKUR links this asymmetry to heat current fluctuations, demonstrating that larger entropy production suppresses fluctuations, making heating more stable than cooling. Our results reveal the thermodynamic basis of asymmetric thermalization and highlight uncertainty relations as key to nonequilibrium quantum dynamics.

The quantum control of spin-correlated radical pairs (SCRPs) holds promise for the targeted manipulation of magnetic field effects, with potential applications ranging from the design of noise-resilient quantum information processors to genetically encodable quantum sensors. However, achieving precise handles over the intricate interplay between coherent electron spin dynamics and incoherent relaxation processes in photoexcited radical-pair reactions requires tractable approaches for numerically obtaining controls for large, complex open quantum systems. Employing techniques relying on full Liouville-space propagators becomes computationally infeasible for large spin systems of realistic complexity. Here, we demonstrate how a control engineering approach based on the Pontryagin Maximum Principle (PMP) can offer a viable alternative by reporting on the successful application of PMP-optimal control to steer the coherent and incoherent spin dynamics of noisy radical pairs. This enables controls for prototypical radical-pair models that exhibit robustness in the face of relevant noise sources and paves the way to incoherent control of radical-pair spin dynamics.

In this work, we study the hardness required to achieve proofs of quantumness (PoQ), which in turn capture (potentially interactive) quantum advantage. A ``trivial'' PoQ is to simply assume an average-case hard problem for classical computers that is easy for quantum computers. However, there is much interest in ``non-trivial'' PoQ that actually rely on quantum hardness assumptions, as these are often a starting point for more sophisticated protocols such as classical verification of quantum computation (CVQC). We show several lower-bounds for the hardness required to achieve non-trivial PoQ, specifically showing that they likely require cryptographic hardness, with different types of cryptographic hardness being required for different variations of non-trivial PoQ. In particular, our results help explain the challenges in using lattices to build publicly verifiable PoQ and its various extensions such as CVQC.

The technique of combining multiple votes to enhance the quality of a decision is the core of boosting algorithms in machine learning. In particular, boosting provably increases decision quality by combining multiple weak learners-hypotheses that are only slightly better than random guessing-into a single strong learner that classifies data well. There exist various versions of boosting algorithms, which we improve upon through the introduction of QuantumBoost. Inspired by classical work by Barak, Hardt and Kale, our QuantumBoost algorithm achieves the best known runtime over other boosting methods through two innovations. First, it uses a quantum algorithm to compute approximate Bregman projections faster. Second, it combines this with a lazy projection strategy, a technique from convex optimization where projections are performed infrequently rather than every iteration. To our knowledge, QuantumBoost is the first algorithm, classical or quantum, to successfully adopt a lazy projection strategy in the context of boosting.

Simulating time evolution under fermionic Hamiltonians is a compelling application of quantum computers because it lies at the core of predicting the properties of materials and molecules. Fermions can be simulated on qubit-based quantum computers using a fermion-to-qubit mapping, subject to an overhead -- the circuit depth on a qubit quantum computer divided by that on a quantum computer built from native fermionic modes -- at worst scaling linearly with the number of modes $N$. Existing approaches that lower this depth overhead usually trade it for space, using $O(N)$ ancilla qubits. We exponentially reduce the worst-case overhead of ancilla-free fermion-to-qubit mappings to $O(\log^2 N)$ by constructing circuits that perform any fermionic permutation on qubits in the Jordan-Wigner encoding in depth $O(\log^2 N)$. We also show that our result generalizes to permutations in any product-preserving ternary tree fermionic encoding. When introducing $O(N)$ ancillas and mid-circuit measurement and feedforward, the overhead reduces to $O(\log N)$. Finally, we show that our scheme can be used to implement the fermionic fast Fourier transform, a key subroutine in chemistry simulation, with overhead $\Theta(\log N)$ without ancillas and $\Theta(1)$ with ancillas, improving exponentially over the best previously known ancilla-free algorithm with overhead scaling linearly with $N$. Our results show that simulating fermions with qubit quantum computers comes at a much lower asymptotic overhead than previously thought.

Holes in Ge/SiGe heterostructures are now a leading platform for semiconductor spin qubits, thanks to the high confinement quality, two-dimensional arrays, high tunability, and larger gate structure dimensions. One limiting factor for the operation of large arrays of qubits is the considerable variation in qubit frequencies or properties resulting from the strongly anisotropic $g$-tensor. We study the $g$-tensors of six and seven qubits in an array with a Y geometry across two devices. We report a mean distribution of the tilts of the $g$-tensor's out-of-plane principal axis of around $1.1 °$, where nearby quantum dots are more likely to have a similar tilt. Independently of this tilt, and unlike simple theoretical predictions, we find a strong in-plane $g$-tensor anisotropy with strong correlations between neighboring quantum dots. Additionally, in one device where the principal axes of all g-tensors are aligned along the [100] crystal direction, we extract the spin-flip tunneling vector from adjacent dot pairs and find a pattern that is consistent with a uniform Dresselhaus-like spin-orbit field. The Y arrangement of the gate layout and quantum dots allows us to rule out local factors like electrostatic confinement shape or local strain as the origin of the preferential direction. Our results reveal long-range correlations in the spin-orbit interaction and $g$-tensors that were not previously predicted or observed, and could prove critical to reliably understand $g$-tensors in germanium quantum dots.

The orbital motion of chargeless bosons, unlike that of electrons, does not generate a magnetic moment and thus cannot directly interact with magnetic fields. Utilizing the Aharonov-Casher effect and perturbation theory, we formulate a proper theory for the magnon orbital angular momentum (OAM) at finite temperatures, explicitly identifying both self-rotation and topological contributions, analogous to the electronic counterpart but with correct bosonic statistics. Comparing with previous studies on magnon OAM, the magnon spin Nernst effect can only be correctly reproduced using the proper theory for magnon OAM. In a two-dimensional honeycomb lattice, we show that the Dzyaloshinskii-Moriya interaction induces a large magnon OAM in both ferromagnetic and antiferromagnetic ground states. Our formulation provides a foundation for studying orbital dynamics of chargeless bosons with intrinsic spin.

The atomtronic matter-wave triple-well transistor is theoretically predicted to exhibit current gain and act as a coherent matter-wave emitter. In this work, we investigate the dynamics of an atomtronic transistor composed of a triple-well potential -- source, gate, and drain -- modeled by the time-dependent Gross-Pitaevskii equation. We systematically explore the dependence of the drain population and the current on the source bias potential and the strength of the interatomic interaction. Our simulations reveal signatures of resonant tunneling when the source chemical potential aligns with discrete energy levels in the gate well, leading to coherent matter-wave emission in the drain. Contrary to previous many-body studies that predicted interaction-induced current gain via coupling to gate well modes, our results suggest that coherence in the drain is primarily governed by single-particle resonances, with no evident broadening from nonlinear coupling.

Bloch oscillations (BOs) describe the coherent oscillatory motion of electrons in a periodic lattice under a constant external electric field. Deviations from pure harmonic wave packet motion or irregular Bloch oscillations can occur due to Zener tunneling (Landau-Zener Transitions or LZTs), with oscillation frequencies closely tied to interband coupling strengths. Motivated by the interplay between flat-band physics and interband coupling in generating irregular BOs, here we investigate these oscillations in Lieb and Kagome lattices using two complementary approaches: coherent transport simulations and scattering matrix analysis. In the presence of unavoidable band touchings, half-fundamental and fundamental BO frequencies are observed in Lieb and Kagome lattices, respectively -- a behavior directly linked to their distinct band structures. When avoided band touchings are introduced, distinct BO frequency responses to coupling parameters in each lattice are observed. Scattering matrix analysis reveals strong coupling and potential LZTs between dispersive bands and the flat band in Kagome lattices, with the quadratic band touching enhancing interband interactions and resulting in BO dynamics that is distinct from systems with linear crossings. In contrast, the Lieb lattice -- a three level system -- shows independent coupling between the flat band and two dispersive bands, without direct LZTs occurring between the two dispersive bands themselves. Finally, to obtain a unifying perspective on these results, we examine BOs during a strain-induced transition from Kagome to Lieb lattices, and link the evolution of irregular BO frequencies to changes in band connectivity and interband coupling.

The Beryllium Electron capture in Superconducting Tunnel junctions (BeEST) experiment uses superconducting tunnel junction (STJ) sensors to search for physics beyond the standard model (BSM) with recoil spectroscopy of the $\mathbf{^7}$Be EC decay into $\mathbf{^7}$Li. A pulsed UV laser is used to calibrate the STJs throughout the experiment with $\sim$20 meV precision. Phase-III of the BeEST experiment revealed a systematic calibration discrepancy between STJs. We found these artifacts to be caused by resistive crosstalk and by intensity variations of the calibration laser. For phase-IV of the BeEST experiment, we have removed the crosstalk by designing the STJ array so that each pixel has its own ground wire. We now also use a more stable UV laser for calibration. The new STJ arrays were fabricated at STAR Cryoelectronics and tested at LLNL and FRIB. They have the same high energy resolution of $\sim$1\textendash2~eV in the energy range of interest below 100~eV as before, and they no longer exhibit the earlier calibration artifacts. We discuss the design changes and the STJ array performance for the next phase of the BeEST experiment.

High-spin states hold significant promise for classical and quantum information storage and emerging magnetic memory technologies. Here, we present a systematic framework for engineering such high-spin magnetic states in dopant clusters formed from substitutional impurities in semiconductors. In single-valley materials such as gallium arsenide, impurity states are hydrogenic and exchange interactions generally favor low-spin configurations, except in special geometries. In contrast, multivalley semiconductors exhibit oscillatory form factors in their exchange couplings, enabling the controlled suppression of selected hopping processes and exchange couplings. Exploiting this feature, we demonstrate how carefully arranged impurities in aluminum arsenide, germanium, and silicon can stabilize ground states with a net spin that scale extensively with system size. Within effective mass theory and the tight-binding approximation for hopping, we construct explicit examples ranging from finite clusters to extended lattices and fractal-like tilings. In two dimensions, we identify several favorable dopant geometries supporting a net spin equal to around half of the fully polarized value in the thermodynamic limit, including one which achieves over $70\%$ polarization. Our results provide a general design principle for harnessing valley degeneracy in semiconductors to construct robust high-spin states and outline a pathway for their experimental realization via precision implantation of dopants.

A key challenge for quantum photonic technologies based on spin qubits is the creation of optically active defects in photonic resonators. Several of the most promising defects for quantum applications are hosted in diamond, and are commonly created through ion implantation and annealing at high temperatures and high vacuum. However, the impact of annealing on photonic resonator quality factor, a critical parameter governing their coupling to defects, has not been reported. In this work, we characterize the effect of annealing at temperatures >1200°C in high vacuum on the quality factors of diamond microdisk resonators. We investigate the optical losses associated with a non-diamond layer formed during annealing, and use Raman spectroscopy to analyze the resonator surface morphology and demonstrate that tri-acid cleaning can restore their optical quality factors. These results show the viability of creating defects in pre-fabricated diamond resonators without degrading their optical properties.

We extend a recently defined measure of symmetry breaking, the entanglement asymmetry, to higher-form symmetries. In particular, we focus on Abelian topological order in two dimensions, which spontaneously breaks a 1-form symmetry. Using the toric code as a primary example, we compute the entanglement asymmetry and compare it to the topological entanglement entropy. We find that while the two quantities are not strictly equivalent, both are sub-leading corrections to the area law and can serve as order parameters for the topological phase. We generalize our results to non-chiral Abelian topological order and express the maximal entanglement asymmetry in terms of the quantum dimension. Finally, we discuss how the scaling of entanglement asymmetry correctly detects topological order in the deformed toric code, where 1-form symmetry breaking persists even in a trivial phase.

Single nuclear spins in silicon are a promising resource for quantum technologies due to their long coherence times and excellent control fidelities. Qubits and qudits have been encoded on donor nuclei, with successful demonstrations of Bell states and quantum memories on the spin-1/2 $^{31}$P and cat-qubits on the spin-7/2 $^{123}$Sb nuclei. Isoelectronic nuclear spins coupled to gate-defined quantum dots, such as the naturally occurring $^{29}$Si isotope, possess no additional charge and allow for the coupled electron to be shuttled without destroying the nuclear spin coherence. Here, we demonstrate the coupling and readout of a spin-9/2 $^{73}$Ge nuclear spin to a gate-defined quantum dot in SiMOS. The $^{73}$Ge nucleus was implanted by isotope-selective ion-implantation. We observe the hyperfine interaction (HFI) to the coupled quantum dot electron and are able to tune it from 180 kHz to 350 kHz, through the voltages applied to the lateral gate electrodes. This work lays the foundation for future spin control experiments on the spin-9/2 qudit as well as more advanced experiments such as entanglement distribution between distant nuclear spins or repeated weak measurements.

Motivated by the profound connection between quantum mechanics and spacetime geometry, particularly the conjectured correspondence between wormholes and quantum entanglement as proposed in the ER=EPR framework, this study aims to investigate the influence of wormhole geometries on quantum information extraction. We examine the correlation-specifically mutual information (MI) and entanglement-extracted by two Unruh-DeWitt (UDW) detectors from the quantum vacuum field in the presence of a BTZ wormhole featuring a null-like throat, also known as an Einstein-Rosen bridge. First, we analyze how the detector's position relative to the wormhole throat and the throat's size affect the extracted MI. Our results indicate that the wormhole enhances MI extraction, with maximal MI achieved when the detectors are located at specific image-symmetric points connected by the wormhole. By analyzing the behavior of the nonlocal contribution term and the classical noise term, it is found that the correlations extracted contain genuine non-classical components. This work highlights the feasibility of extracting quantum correlations through null-like wormhole geometries and provides a novel perspective for probing the potential relationship between spacetime topology and the nonlocal characteristics of quantum mechanics.

Many quantum gravitational frameworks, such as DBI inflation, k-essence, and effective field theories obtained by integrating out heavy modes, can lead to a non-trivial sound speed. Meanwhile, our universe can be described as an open system. Under the non-trivial sound speed, we employ the method of open quantum systems combined with Arnoldi iterations to study the Krylov complexity throughout the early universe, including the inflationary, radiation-dominated, and matter-dominated epochs. A key ingredient in our analysis is the open two-mode squeezed state formalism and the generalized Lanczos algorithm. To numerically compute the Krylov complexity, we are the first time to derive the evolution equations for the parameters $r_k$ and $\phi_k$ within an open two-mode squeezed state. Our results indicate that the Krylov complexity exhibits a similar trend in both the standard case and the case with non-trivial sound speed. To distinguish between these two scenarios, we also investigate the Krylov entropy for completeness. The evolution of the Krylov entropy shows a clear difference between the standard case and the non-trivial sound speed case. Furthermore, based on the behavior of the Lanczos coefficients, we find that the case of non-trivial sound speed behaves as a maximally chaotic system. However, our numerical results suggest that the Krylov complexity does not saturate to a constant value due to the huge expansion of spacetime background. This study offers a new perspective for exploring the early universe through the quantum information.

We investigate the phenomenon of spacetime-localized response in a quantum critical spin system, with particular attention to how it depends on the spatial profile and operator content of the applied perturbation, as well as its robustness against increase of amplitude and temporal discretization. Motivated by recent theoretical proposals linking such response patterns to the anti-de Sitter/conformal field theory correspondence, we numerically analyze the real-time dynamics of the one-dimensional transverse-field Ising model at criticality using the time-evolving block decimation algorithm. We find that sharply localized and periodically recurring responses emerge only for specific types of perturbations, namely those that correspond to local density fields in the continuum limit. In contrast, perturbations involving other spin components produce conventional propagating excitations without localization. Furthermore, we demonstrate that the response remains qualitatively robust when the time-dependent perturbation is approximated by a piecewise-linear function, highlighting the practical relevance of our findings for quantum simulation platforms with limited temporal resolution. Our results clarify the operator dependence of emergent bulk-like dynamics in critical spin chains and offer guidance for probing holographic physics in experimental settings.

Gluing theorem for random unitaries [Schuster, Haferkamp, Huang, QIP 2025] have found numerous applications, including designing low depth random unitaries [Schuster, Haferkamp, Huang, QIP 2025], random unitaries in ${\sf QAC0}$ [Foxman, Parham, Vasconcelos, Yuen'25] and generically shortening the key length of pseudorandom unitaries [Ananth, Bostanci, Gulati, Lin EUROCRYPT'25]. We present an alternate method of combining Haar random unitaries from the gluing lemma from [Schuster, Haferkamp, Huang, QIP 2025] that is secure against adversaries with inverse query access to the joined unitary. As a consequence, we show for the first time that strong pseudorandom unitaries can generically have their length extended, and can be constructed using only $O(n^{1/c})$ bits of randomness, for any constant $c$, if any family of strong pseudorandom unitaries exists.

Localized quantum emitters in transition-metal dichalcogenides (TMDs) have recently emerged as solid-state candidates for on-demand sources of single photons. Due to the role of strain in the site-selective creation of TMD emitters, their hybrid integration into photonic structures such as cavities and waveguides is possible using pick-and-place methods. Here we investigate quantum emission from a hybrid structure consisting of a monolayer of WSe2 interfaced with horizontally aligned InP nanowires (NWs). Our experiments reveal multiple narrow and bright emission peaks in the 715-785 nm spectral range and g(2)(0) as low as 0.049, indicating strong antibunching and good single photon purity. The faceted nature of III-V NWs provides unique opportunities for strain engineering, including the potential for placement of emitters on the top surface for optimal coupling. Our findings pave the way for realizing hybrid quantum light sources for integrated quantum photonics that could combine III-V quantum dots with TMD emitters into a single platform.

In the context of entanglement in relativistic $2\to 2$ scattering described by a perturbative $S$-matrix, we derive analytically the concurrence for a mixed final state of two qubits corresponding to a discrete quantum number of the scattered particles. Given an initial product state, the derived concurrence depends at the leading order on the real part of the inelastic forward amplitude and the initial state only. We also point out that the real part of the forward amplitude provides a subleading correction to the linearized entropy, reducing it by an amount that, for a computational-basis state, is equivalent to the relative entropy of coherence. We illustrate our findings with two examples of phenomenological interest: high-energy scattering of two scalar fields in the two-Higgs doublet model, and high-energy electron-positron annihilation.

We demonstrate the realization of a discrete-time crystal (DTC) phase in a family of periodically driven, one-dimensional quadratic lattice Hamiltonians that can be obtained using spin chains. These interactions preserve integrability while opening controllable gaps at resonant quasienergies and pinning the emergent quasienergy modes that are responsible for subharmonics. We demonstrate that the DTC phase is rigid in the parameter space of transverse field and an additional interaction like NNN coupling strength, with the drive frequency optimized to produce the strongest subharmonic response. We also provide a detailed phase portrait of the model, exhibiting a variety of new dynamical phases, such as a fragile time crystal and both spin-liquid and paramagnetic phases, as well as sharp quantum phase transitions between them. Finite-size scaling of the Floquet quasienergy splitting between the emergent subharmonic mode and its conjugate shows that the DTC lifetime diverges exponentially with system size. Our work thus establishes a novel mechanism for realizing robust, long-lived DTCs in one dimension, and paves the way for their experimental realization in near-term quantum simulators. Motivation for this work stems from the limitations of disorder-based stabilization schemes that rely on many-body localization and exhibit only prethermal or finite-lived plateaus, eventually restoring ergodicity. Disorder-free routes are therefore highly desirable. Integrable (or Floquet-integrable) systems provide an attractive alternative because their extensive set of conserved quantities and constrained scattering strongly restrict thermalization channels. Our construction exploits these integrable restrictions together with short-range NNN engineering to produce a clean, robust DTC that avoids the prethermal fragility of disordered realizations.

Using the gauge-gravity duality, we study the electromagnetic instability of vacuum with instantons in holographic plasma. The model we employ is the D(-1)-D3 brane system in which the D(-1)-branes correspond to the instantons in holography. To take into account the flavored quarks, the coincident probe D7-branes as flavors are embedded into the bulk geometry so that the effective electromagnetic Lagrangian with flavors corresponds to the action of the D7-branes according to gauge-gravity duality. We numerically evaluate the vacuum decay rate, the critical electric field and the V-A curve of the vacuum by using the D7-brane action with various values of the electromagnetic field. It implies the particles in the plasma acquire an effective mass in the presence of instantons as it is expected in the quantum field theory, and the plasma trends to become insulating when the electric field is small. This work reveals the relation between electromagnetic and instantonic properties of the vacuum in the plasma.

We present the first construction of a computational Certified Deletion Property (CDP) achievable with classical communication, derived from the compilation of the non-local Magic Square Game (MSG). We leverage the KLVY compiler to transform the non-local MSG into a 2-round interactive protocol, rigorously demonstrating that this compilation preserves the game-specific CDP. Previously, the quantum value and rigidity of the compiled game were investigated. We emphasize that we are the first to investigate CDP (local randomness in [Fu and Miller, Phys. Rev. A 97, 032324 (2018)]) for the compiled game. Then, we combine this CDP with the framework [Kitagawa, Morimae, and Yamakawa, Eurocrypt 2025] to construct Secure Key Leasing with classical Lessor (cSKL). SKL enables the Lessor to lease the secret key to the Lessee and verify that a quantum Lessee has indeed deleted the key. In this paper, we realize cSKL for PKE, PRF, and digital signature. Compared to prior works for cSKL, we realize cSKL for PRF and digital signature for the first time. In addition, we succeed in weakening the assumption needed to construct cSKL.

The simplest, algebraic quantum-electrodynamical corrections, due to the double-negative energy subspace and instantaneous interactions, are computed to the no-pair Dirac-Coulomb(-Breit) energy of two-spin-1/2-fermion systems. Numerical results are reported for two-electron atoms with a clamped nucleus and positronium-like genuine two-particle systems. The Bethe-Salpeter equation provides the theoretical framework, and numerical methods have been developed for its equal-time time-slice. In practice, it requires solving a sixteen-component eigenvalue equation with a two-particle Dirac Hamiltonian, including the appropriate interaction. The double-pair corrections can either be included in the interaction part of the eigenvalue equation or treated as a perturbation to the no-pair Hamiltonian. The numerical results have an $\alpha$ fine-structure constant dependence that is in excellent agreement with the known $\alpha^3E_\mathrm{h}\$-order double-pair correction of non-relativistic quantum electrodynamics.

The semi-empirical Pariser-Parr-Pople (PPP) Hamiltonian is reviewed for its ability to provide a minimal model of the chemistry of conjugated $\pi$-electron systems, and its current applications and limitations are discussed. From its inception, the PPP Hamiltonian has helped in the development of new computational approaches in instances where compute is constrained due to its inherent approximations that allow for an efficient representation and calculation of many systems of chemical and technological interest. The crucial influence of electron correlation on the validity of these approximations is discussed, and we review how PPP model exact calculations have enabled a deeper understanding of conjugated polymer systems. More recent usage of the PPP Hamiltonian includes its application in high-throughput screening activities to the inverse design problem, which we illustrate here for two specific fields of technological interest: singlet fission and singlet-triplet inverted energy gap molecules. Finally, we conjecture how utilizing the PPP model in quantum computing applications could be mutually beneficial.

In this paper, for $\alpha\in(0,\infty)\setminus\{1\}$, $p>0$ and positive semidefinite matrices $A$ and $B$, we consider the quasi-extension $\mathcal{M}_{\alpha,p}(A,B):=\mathcal{M}_\alpha(A^p,B^p)^{1/p}$ of several $\alpha$-weighted geometric type matrix means $\mathcal{M}_\alpha(A,B)$ such as the $\alpha$-weighted geometric mean in Kubo--Ando's sense, the Rényi mean, etc. The log-majorization $\mathcal{M}_{\alpha,p}(A,B)\prec_{\log}\mathcal{N}_{\alpha,q}(A,B)$ is examined for pairs $(\mathcal{M},\mathcal{N})$ of those $\alpha$-weighted geometric type means. The joint concavity/convexity of the trace functions $\mathrm{Tr}\,\mathcal{M}_{\alpha,p}$ is also discussed based on theory of quantum divergences.

Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and a context-aware proof calculus that is conservative in the flat limit. We formalize CBL-SAT and basic complexity (NP-complete in general) and present operational operators (CBL-AC and CBL-CONS) that prune contradictions earlier on classical hardware. We model noise with iid, AR(1)-correlated, and adversarial bounded perturbations and provide permutation-based significance with Benjamini-Hochberg FDR control. A Colab-ready notebook (ancillary files) regenerates all figures and statistics. We position CBL relative to KCBS, CSW, and sheaf frameworks and outline links to SAT/CSP and robustness/adapter stability in large language models.

Doped Mott insulators host intertwined spin-charge phenomena that evolve with temperature and can culminate in stripe order or superconductivity at low temperatures. The two-dimensional $t$-$J$ model captures this interplay yet finite-temperature, infinite-size calculations remain difficult. Using purification represented by a tensor network - an infinite projected entangled-pair state (iPEPS) ansatz - we simulate the $t$-$J$ model at finite temperature directly in the thermodynamic limit, reaching temperatures down to one tenth of the hopping rate and hole concentrations up to one quarter of the lattice sites. Beyond specific heat, uniform susceptibility, and compressibility, we introduce dopant-conditioned multi-point correlators that map how holes reshape local exchange. Nearest-neighbor hole pairs produce a strong cooperative response that reinforces antiferromagnetism on the adjacent parallel bonds, and single holes weaken nearby antiferromagnetic bonds; d-wave pairing correlations remain short-ranged over the same window. These results provide experiment-compatible thermodynamic-limit benchmarks and establish dopant-conditioned correlators as incisive probes of short-range spin-texture reorganization at finite temperature.

Horn's problem is concerned with characterizing the eigenvalues $(a,b,c)$ of Hermitian matrices $(A,B,C)$ satisfying the constraint $A+B=C$ and forming the edges of a triangle in the space of Hermitian matrices. It has deep connections to tensor product invariants, Littlewood-Richardson coefficients, geometric invariant theory and the intersection theory of Schubert varieties. This paper concerns the tetrahedral Horn problem which aims to characterize the tuples of eigenvalues $(a,b,c,d,e,f)$ of Hermitian matrices $(A,B,C,D,E,F)$ forming the edges of a tetrahedron, and thus satisfying the constraints $A+B=C$, $B+D=F$, $D+C=E$ and $A+F=E$. Here we derive new inequalities satisfied by the Schur-polynomials of such eigenvalues and, using eigenvalue estimation techniques from quantum information theory, prove their satisfaction up to degree $k$ implies the existence of approximate solutions with error $O(\ln k / k)$. Moreover, the existence of these tetrahedra is related to the semiclassical asymptotics of the $6j$-symbols for the unitary group $U(n)$, which are maps between multiplicity spaces that encode the associativity relation for tensor products of irreducible representations. Using our techniques, we prove the asymptotics of norms of these $6j$-symbols are either inverse-polynomial or exponential depending on whether there exists such tetrahedra of Hermitian matrices.

We introduce a general corner transfer matrix renormalization group algorithm tailored to projected entangled-pair states on the triangular lattice. By integrating automatic differentiation, our approach enables direct variational energy minimization on this lattice geometry. In contrast to conventional approaches that map the triangular lattice onto a square lattice with diagonal next-nearest-neighbour interactions, our native formulation yields improved variational results at the same bond dimension. This improvement stems from a more faithful and physically informed representation of the entanglement structure in the tensor network and an increased number of variational parameters. We apply our method to the antiferromagnetic nearest-neighbour Heisenberg model on the triangular and kagome lattice, and benchmark our results against previous numerical studies.

Quantum entanglement is difficult to teach because it is microscopic and non classical. We present interactive electronic dice that simulate core quantum ideas through haptic interaction and visual feedback. Each die represents a six state system with a superposition display and basis dependent measurement. A pair of dice can be prepared in an entangled mode that yields anti correlated outcomes which sum to seven when measured in the same colour basis while remaining uncorrelated across different bases. The platform supports classroom demonstrations from basic superposition and measurement to simplified quantum key distribution with single die and entanglement based protocols. The design uses standard components, two custom PCBs, orientation sensing, cryptographic quality randomness, and low power wireless proximity detection. All hardware files and code are open source to enable adoption. Initial implementations with university and secondary school audiences suggest that the tangible and visual nature of the dice helps learners form intuitive models of superposition, measurement, and entanglement correlations.

We introduce a theory for computational control, consisting of seven naturally interpretable equations. Adding these to a prop of base circuits constructs controlled circuits, borne out in examples of reversible Boolean circuits and quantum circuits. We prove that this syntactic construction semantically corresponds to taking the free rig category on the base prop.

Vacuum cavity control of quantum materials is the engineering of quantum materials systems through electromagnetic zero-point fluctuations. In this work we articulate a generic mechanism for vacuum optical control of correlated electronic order: Casimir control, where the zero-point energy of the electromagnetic continuum, the Casimir energy, depends on the properties of the material system. To assess the experimental viability of this mechanism we focus on the Casimir stabilization of fluctuating nematic order. In nematic Fermi liquids, different orientations of the electronic order are often energetically degenerate. Thus, while local domains of fixed orientation may form, thermal disordering inhibits long range order. By engineering the electromagnetic environment of the electronic system, however, we show that the Casimir energy can be used as a tool to preferentially stabilize particular orientations of the nematic order. As a concrete example, we examine the interplay between a birefringent crystal -- which sources an anisotropic electromagnetic environment -- and a quantum Hall stripe system, an archetypal nematic Fermi fluid. We show that for experimentally feasible setups, the anisotropy induced by the orientation dependent Casimir energy can be $10^4$ times larger than other mechanisms known to stabilize quantum Hall stripes. This finding convincingly implies that our setting may be realized with currently available experimental technology. Having demonstrated that the Casimir energy can be used to stabilize fluctuating nematic order, we close by discussing the implications for recent terahertz cavity experiments on quantum Hall stripes, as well as pave the road towards broader Casimir control of competing correlated electronic phases.

The hierarchical equations of motion (HEOM) approach can describe the reduced dynamics of a system simultaneously coupled to multiple bosonic and fermionic environments. The complexity of exactly describing the system-environment interaction with the HEOM method usually results in time-consuming calculations and a large memory cost. Here, we introduce an open-source software package called HierarchicalEOM$.$jl: a Julia framework integrating the HEOM approach. HierarchicalEOM$.$jl features a collection of methods to compute bosonic and fermionic spectra, stationary states, and the full dynamics in the extended space of all auxiliary density operators (ADOs). The required handling of the ADOs multi-indexes is achieved through a user-friendly interface. We exemplify the functionalities of the package by analyzing a single impurity Anderson model, and an ultra-strongly coupled charge-cavity system interacting with bosonic and fermionic reservoirs. HierarchicalEOM$.$jl achieves a significant speedup with respect to the corresponding method in the Quantum Toolbox in Python (QuTiP), upon which this package is founded.

In this paper we study the autoparallelity w.r.t. the e-connection for an information-geometric structure called the SLD structure, which consists of a Riemannian metric and mutually dual e- and m-connections, induced on the manifold of strictly positive density operators. Unlike the classical information geometry, the e-connection has non-vanishing torsion, which brings various mathematical difficulties. The notion of e-autoparallel submanifolds is regarded as a quantum version of exponential families in classical statistics, which is known to be characterized as statistical models having efficient estimators (unbiased estimators uniformly achieving the equality in the Cramer-Rao inequality). As quantum extensions of this classical result, we present two different forms of estimation-theoretical characterizations of the e-autoparallel submanifolds. We also give several results on the e-autoparallelity, some of which are valid for the autoparallelity w.r.t. an affine connection in a more general geometrical situation.

Theoretically understanding and experimentally characterizing and modifying the underlying Hamiltonian of a quantum system is of utmost importance in achieving high-fidelity quantum gates for quantum computing. In this work, we explore the use of dynamical decoupling (DD) in characterizing and suppressing undesired two-qubit couplings as well as the underlying single-qubit decoherence, both significant hurdles to achieving precise quantum control and realizing quantum computing on many hardware prototypes. Through discrete search of dynamical decoupling sequences, we identify sequences that protect against decoherence and selectively target unwanted two-qubit interactions of general form. On a transmon-qubit-based superconducting quantum device, we identify separate white and 1/f noise components underlying the single-qubit decoherence and a static ZZ coupling between pairs of qubits. A family of syncopated dynamical decoupling sequences is found and their efficiency demonstrated in two-qubit benchmarking experiments. The syncopated decoupling technique significantly boosts performance in a realistic algorithmic quantum circuit.

Quantum circuits for loading probability distributions into quantum states are essential subroutines in quantum algorithms used in physics, finance engineering, and machine learning. The ability to implement these with high accuracy in low-depth quantum circuits is a critical issue. We propose a novel quantum state preparation method for probability distribution with reflection symmetry using matrix product states. By considering reflection symmetry, our method reduces the entanglement of probability distributions and improves the accuracy of approximations by matrix product states. As a result, we improved the accuracy by two orders of magnitude over existing methods using matrix product states. Our approach, characterized by linear scalability with qubit count, is highly advantageous for noisy quantum devices. Also, our demonstration results reveal that the approximation accuracy in tensor networks depends heavily on the bond dimension, with minimal reliance on the number of qubits. Our method is demonstrated for a normal distribution encoded into 10 and 20 qubits on a real quantum processor.

I present an accreditation protocol (a variety of quantum verification) where error is assumed to be adversarial (in contrast to the assumption error is implemented by identical CPTP maps used in previous accreditation protocols) - albeit slightly modified to reflect physically motivated error assumptions. This is achieved by upgrading a pre-existing accreditation protocol (from [S. Ferracin et al. Phys. Rev. A 104, 042603 (2021)]) to function correctly in the face of adversarial error, with no diminution in efficiency or suitability for near-term usage.

Quantum computing is rapidly advancing, harnessing the power of qubits' superposition and entanglement for computational advantages over classical systems. However, scalability poses a primary challenge for these machines. By implementing a hybrid workflow between classical and quantum computing instances, D-Wave has succeeded in pushing this boundary to the realm of industrial use. Furthermore, they have recently opened up to mixed integer linear programming (MILP) problems, expanding their applicability to many relevant problems in the field of optimisation. However, the extent of their suitability for diverse problem categories and their computational advantages remains unclear. This study conducts a comprehensive examination by applying a selection of diverse case studies to benchmark the performance of D-Wave's hybrid solver against that of industry-leading solvers such as CPLEX, Gurobi, and IPOPT. The findings indicate that D-Wave's hybrid solver is currently most advantageous for integer quadratic objective functions and shows potential for quadratic constraints. To illustrate this, we applied it to a real-world energy problem, specifically the MILP unit commitment problem. While D-Wave can solve such problems, its performance has not yet matched that of its classical counterparts.

We study the size and shape statistics of ground state fuzzy spheres when projected onto the transverse plane, utilizing the regularized SU(N=2) matrix model in D=(1+3)-dimensional spacetime. We show that they appear as ellipses, from matrix/membrane correspondence. With our numerical and analytical approximation for the ground state wavefunction, we provide estimations for their expectation surface areas, perimeters, eccentricities, and shape-parameters. These geometric constants of quantum membranes deviate drastically from classical mechanics.

A crucial ingredient for scalable fault-tolerant quantum computing is the construction of logical qubits with low error rates and intrinsic noise protection. We propose a cross-platform construction for such hardware-level noise-protection in which the qubits are protected from depolarizing (relaxation) and dephasing errors induced by local noise. These logical qubits arise from the entanglement between two internal degrees of freedom, hence - entanglemons. Our construction is based on the emergence of collective degrees of freedom from a generalized coherent state construction, similar in spirit to spin coherent states, of a set of such internally entangled units. These degrees of freedom, for a finite number of units, parametrize the quantized version of complex projective space $\mathbb{C}$P(3). The noise protection of the entanglemon qubit is then a consequence of a weakly coupled emergent degree of freedom arising due to the non-linear geometry of complex projective space. We present two simple models for entanglemons which are platform agnostic, provide varying levels of protection and in which the qubit basis states are the two lowest energy states with a higher energy gap to other states. We end by commenting on how entanglemons could be realized in platforms ranging from superconducting circuits and trapped ion platforms to possibly also quantum Hall skyrmions in graphene and quantum dots in semiconductors. The inherent noise protection in our models combined with the platform agnosticism highlights the potential of encoding information in additional weakly coupled emergent degrees of freedom arising in non-linear geometrical spaces and curved phase spaces, thereby proposing a different route to achieve scalable fault-tolerance.

We construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) commitments and QCCC multiparty non-interactive key exchange exist. We also construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QMA}$, but quantum lightning (a stronger variant of quantum money) exists. This extends previous work by Kretschmer [Kretschmer, TQC22], which showed that there is a quantum oracle relative to which $\mathbf{BQP}=\mathbf{QMA}$ but pseudorandm unitaries exist. We also show that (poly-round) QCCC key exchange, QCCC commitments, and two-round quantum key distribution can all be used to build one-way puzzles. One-way puzzles are a version of ``quantum samplable'' one-wayness and are an intermediate primitive between pseudorandom state generators and EFI pairs, the minimal quantum primitive. In particular, one-way puzzles cannot exist if $\mathbf{BQP}=\mathbf{PP}$. Our results together imply that aside from pseudorandom state generators, there is a large class of quantum cryptographic primitives which can exist even if $\mathbf{BQP} = \mathbf{QCMA}$, but are broken if $\mathbf{BQP} = \mathbf{PP}$. Furthermore, one-way puzzles are a minimal primitive for this class. We denote this class ``CountCrypt''.

We utilize the symmetry groups of regular tessellations on two-dimensional surfaces of different constant curvatures, including spheres, Euclidean planes and hyperbolic planes, to encode a qubit or qudit into the physical degrees of freedom on these surfaces, which we call tessellation codes. We show that tessellation codes exhibit decent error correction properties by analysis via geometric considerations and the representation theory of the isometry groups on the corresponding surfaces. Interestingly, we demonstrate how this formalism enables the implementation of certain logical operations through geometric rotations of surfaces in real space, opening a new approach to logical quantum computation. We provide a variety of concrete constructions of such codes associated with different tessellations, which give rise to different logical groups. This formalism sheds a new light on quantum code and logical operation construction.

Aaronson, Atia, and Susskind (2020) established that efficiently mapping between quantum states $|\psi\rangle$ and $|\phi\rangle$ is computationally equivalent to distinguishing their superpositions $|\psi\rangle \pm |\phi\rangle$. We generalize this insight into a broader duality principle, wherein manipulating quantum states in one basis is equivalent to extracting their value in a complementary basis. This general duality principle states that the ability to implement a unitary representation of a group is computationally equivalent to the ability to perform a Fourier subspace extraction from its irreducible representations. Building on our duality principle, we present the following applications: * We extend the construction of publicly-key quantum money of Zhandry (2024) from Abelian group actions to a construction of quantum lightning from non-Abelian group actions, and eliminate Zhandry's reliance on a black-box model for justifying security. Instead, we prove a direct reduction to a computational assumption -- the pre-action security of cryptographic group actions. Our construction is realizable with symmetric group actions, including those implicit in the McEliece cryptosystem. * We provide an alternative quantum lightning construction from one-way homomorphisms, with security holding under certain conditions. This scheme shows equivalence among four security notions: quantum lightning security, worst-case and average-case cloning security, and security against preparing a canonical state. * We formalize the notion of quantum fire, states that are efficiently clonable, but not efficiently telegraphable. These states can be spread like fire, provided they are kept alive quantumly and do not decohere. The only previously known construction relied on a unitary quantum oracle, whereas we present the first candidate construction of quantum fire using a classical oracle.

We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum speedups, extending a central notion of symmetric computation studied in the classical setting. Our results establish that symmetric quantum circuits are fundamentally more powerful than their classical counterparts. First, we give efficient symmetric circuits for key quantum techniques such as amplitude amplification, phase estimation and linear combination of unitaries. In addition, we show how the task of symmetric state preparation can be performed efficiently in several natural cases. Finally, we demonstrate an exponential separation in the symmetric setting for the problem XOR-SAT, which requires exponential-size symmetric classical circuits but can be solved by polynomial-size symmetric quantum circuits.

The efficient optimization of variational quantum algorithms (VQAs) is critical for their successful application in quantum computing. The Quantum Natural Gradient (QNG) method, which leverages the geometry of quantum state space, has demonstrated improved convergence compared to standard gradient descent [Quantum 4, 269 (2020)]. In this work, we introduce the Modified Conjugate Quantum Natural Gradient (CQNG), an optimization algorithm that integrates QNG with principles from the nonlinear conjugate-gradient method. Unlike QNG, which employs a fixed learning rate, CQNG dynamically adjusts its hyperparameters at each step, enhancing both efficiency and flexibility. Numerical simulations show that CQNG achieves faster convergence and reduces quantum-resource requirements compared to QNG across various optimization scenarios, even when strict conjugacy conditions are not fully satisfied--hence the term ``Modified Conjugate.'' These results highlight CQNG as a promising optimization technique for improving the performance of VQAs.

The ability to physically move qubits within a register allows the design of hardware-specific error-correction codes, which can achieve fault-tolerance while respecting other constraints. In particular, recent advancements have demonstrated the shuttling of electron and hole spin qubits through a quantum dot array with high fidelity. It is therefore timely to explore error correction architectures consisting merely of two parallel quantum dot arrays, an experimentally validated architecture compatible with classical wiring and control constraints. Upon such an architecture, we develop a suite of heuristic methods for compiling any Calderbank-Shor-Steane (CSS) error-correcting code's syndrome-extraction circuit to run with a reduced number of shuttling operations. We demonstrate how column-regular qLDPC codes can be compiled in a provably minimal number of shuttles that is exactly equal to the column weight of the code when Shor-style syndrome extraction is used. We provide tables stating the number of required shuttles for many contemporary codes of interest. In addition, we provide a proof of the NP hardness of minimizing the number of shuttle operations for general codes, even when using Shor syndrome extraction. We also discuss how one could get around this by placing blanks in the ancilla array to achieve minimal shuttles with Shor syndrome extraction on any CSS code, at the cost of longer ancilla arrays

Understanding the effects of noise on quantum computations is fundamental to the development of quantum hardware and quantum algorithms. Simulation tools are essential for quantitatively modelling these effects, yet unless artificial restrictions are placed on the circuit or noise model, accurately modelling noisy quantum computations is an extremely challenging task due to unfavourable scaling of required computational resources. Tensor network methods offer a viable solution for simulating computations that generate limited entanglement or that have noise models which yield low gate fidelities. However, in the most interesting regime of entangling circuits (with high gate fidelities) relevant for error correction and mitigation tensor network simulations often achieve poor accuracy. In this work we develop and numerically test a method for significantly improving the accuracy of tensor network simulations of noisy quantum circuits in the low-noise (i.e. high gate-fidelity) regime. Our method comes with the advantages that it (i) allows for the simulation of quantum circuits under generic types of noise model, (ii) is especially tailored to the low-noise regime, and (iii) retains the benefits of tensor network scaling, enabling efficient simulations of large numbers of qubits. We build upon the observations that adding extra noise to a quantum circuit makes it easier to simulate with tensor networks, and that the results can later be reliably extrapolated back to the low-noise regime of interest. These observations form the basis for a novel emulation technique that we call non-zero noise extrapolation, in analogy to the quantum error mitigation technique of zero-noise extrapolation.

We present EHands, a quantum-native protocol for implementing multivariable polynomial transformations on quantum processors. The protocol introduces four fundamental, reversible operators: multiplication, addition, negation, and parity flip, and employs the Expectation Value ENcoding (EVEN) scheme to represent real numbers as quantum states. Unlike discretization or binary encoding methods, EHands operates directly on vectorized real-valued inputs prepared in the initial state and applies a shallow quantum circuit that depends only on the polynomial coefficients. The result is obtained from the expectation value measured on a single qubit, enabling efficient parallel evaluation of a polynomial across multiple data points using a single circuit. We introduce both a reversible implementation for degree-$d$ polynomials, requiring $3d$ qubits, and a non-reversible variant that uses qubit resets to reduce the requirements to $d+1$ qubits. Both implementations exhibit linear depth scaling in $d$ and are explicitly decomposed into one- and two-qubit gates for direct execution on current quantum processing units. The protocol's effectiveness is demonstrated through experimental validation on IBM's Heron-class quantum processors, showing reliable polynomial approximations of functions like ReLU and arctan.

Retrieving classical information from quantum systems is central to quantum information processing. As a more general task than quantum state discrimination, which focuses on identifying the exact state, quantum state exclusion only requires ruling out options, revealing fundamental limits of information extraction from quantum systems. In this work, we study the conclusive exclusion of quantum states generated by group actions, establishing explicit criteria for when such exclusion is possible. For systems with complex symmetries, including finite and compact Lie groups, we derive a sufficient condition for conclusive exclusion based on the initial state's amplitudes and the group's structure. As applications to special groups such as Abelian groups, we establish necessary and sufficient conditions for conclusive state exclusion and generalize the Pusey-Barrett-Rudolph result to a wider range of scenarios. Finally, we explore zero-error communication via conclusive exclusion of quantum states and derive a lower bound on the feedback-assisted and non-signalling-assisted zero-error capacity of classical-quantum channels generated by group actions.

Quantum battery (QB) is an application of quantum thermodynamics which uses quantum effects to store and transfer energy, overcoming the limitations of classical batteries and potentially improving performance. However, due to the interaction with the external environment, it will lead to decoherence and thus reduce the lifetime of QBs. Here, we propose suppressing the environmental dissipation in the energy-storage process of the QB by exploiting the electromagnetically-induced transparency (EIT) and bound states. By constructing a hybrid system composed of a four-level atom and a coupled-cavity array, two bound states are formed in the system when the energy of the QB is in the energy band of the cavity array. Due to the bound states and the EIT effect, the ambient dissipation is significantly suppressed, which improves the lifetime of the QB. In addition, we show that when the energy of the QB is in resonance with the cavity, the ergotropy of the QB reaches the maximum. Furthermore, there exists an optimal coupling strength between two neighbouring cavities which helps improve the performance of the QB. These discoveries may shed the light on the design of high-efficiency QBs.

High-energy colliders enable the testing of quantum mechanics at its most fundamental level, in the presence of strong and electroweak interactions, with systems that consist of qubits (fermions) and qutrits (massive spin-1 bosons). Quantum state tomography at colliders enables the witnessing of entanglement and Bell non-locality, two defining characteristics of quantum mechanics. We offer a comprehensive explanation of the underlying principles and the methods employed to achieve this remarkable feat.

Infinity is central to deriving macroscopic irreversibility from reversible microscopic laws across mathematics, theoretical computer science and physics. In analysis, infinite processes - such as Dedekind cuts and Cauchy sequences - construct real numbers as equivalence classes of rational approximations, bridging discrete rationals to the continuous real line. In quantum mechanics, infinite tensor products model nested measurements, where sectorization partitions the Hilbert space into equivalence classes, reconciling unitary evolution with wavefunction collapse. In statistical mechanics, macrostates emerge as equivalence classes of microstates sharing identical macroscopic properties, providing the statistical basis for thermodynamic irreversibility despite reversible dynamics. Equivalence relations formalize For-All-Practical-Purposes (FAPP) indistinguishability, reflecting operational limits on precision and observation. Together, these examples reveal a unified framework where infinity and equivalence underpin emergent macroscopic behavior from microscopic reversibility.

Quantum Max Cut (QMC) problem for systems of qubits is an example of a 2-local Hamiltonian problem, and a prominent paradigm in computational complexity theory. This paper investigates the algebraic structure of a higher-dimensional analog of the QMC problem for systems of qudits. The Quantum Max d-Cut (d-QMC) problem asks for the largest eigenvalue of a Hamiltonian on a graph with n vertices whose edges correspond to swap operators acting on $(\mathbb C^d)^{\otimes n}$. The algebra generated by the swap operators is identified as a quotient of a free algebra modulo symmetric group relations and a single additional relation of degree d. This presentation leads to a tailored hierarchy of semidefinite programs, leveraging noncommutative polynomial optimization (NPO) methods, that converges to the solution of the d-QMC problem. For a large class of complete bipartite graphs, exact solutions for the d-QMC problem are derived using the representation theory of symmetric groups and Littlewood-Richardson coefficients. Lastly, the paper addresses a refined d-QMC problem focused on finding the largest eigenvalue within each isotypic component (irreducible block) of the graph Hamiltonian. It is shown that the spectrum of the star graph Hamiltonian distinguishes between isotypic components of the 3-QMC problem. For general d, low-degree relations for separating isotypic components are presented, enabling adaptation of the global NPO hierarchy to efficiently compute the largest eigenvalue in each isotypic component.

Out-of-time order correlators (OTOCs) are crucial tools for studying quantum chaos as they show distinct scrambling behavior for chaotic Hamiltonians. We calculate OTOC and analyze the quantum information scrambling in atom-field and spin-spin interaction models, which are open-system models and exhibit non-Markovian behavior. We also examine the Loschmidt echo for these models and comment on their chaotic nature. The commutator growth of two local operators, which is upper bounded by the Lieb-Robinson bound, is studied for these models, and the patterns of scrambling are investigated.

We demonstrate longtime coherent subharmonic motion of a many-boson system subjected to an external time-periodic driving force. The underlying mechanism is exemplified numerically through analysis of a periodically driven Bose-Hubbard dimer, and clarified conceptually by semiclassical requantization of invariant tubes pertaining to the system's mean-field description. In this way, one arrives at pre-Floquet states that relate to the actual many-body Floquet states in a manner similar to the relation of site-localized Wannier states to lattice-extended Bloch states in solid-state physics. It is argued that even high-order subharmonic response can be systematically engineered, and be observed experimentally, with weakly interacting Floquet condensates comprising a sufficiently large number of particles.

Semiconductors are among the most promising platforms to implement large-scale quantum computers, as advanced manufacturing techniques allow fabrication of large quantum dot arrays. Various qubit encodings can be used to store and manipulate quantum information on these quantum dot arrays. Regardless of qubit encoding, precise control over the exchange interaction between electrons confined in quantum dots in the array is critical. Furthermore, it is necessary to execute high-fidelity quantum operations concurrently to make full use of the limited coherence of individual qubits. Here, we demonstrate the parallel operation of two exchange-only qubits, consisting of six quantum dots in a linear arrangement. Using randomized benchmarking techniques, we show that issuing pulses on the five barrier gates to modulate exchange interactions in a maximally parallel way maintains the quality of qubit control relative to sequential operation. The techniques developed to perform parallel exchange pulses can be readily adapted to other quantum-dot based encodings. Moreover, we show the first experimental demonstrations of an iSWAP gate and of a charge-locking Pauli spin blockade readout method. The results are validated using cross-entropy benchmarking, a technique useful for performance characterization of larger quantum computing systems; here it is used for the first time on a quantum system based on semiconductor technology.

We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an $N$-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves separability and allows to characterize the entanglement of the original multipartite state. In particular, we establish a connection between the border rank and the Schmidt rank, and derive lower bounds on entanglement measures. Finally, we reveal the existence of entangled symmetric subspaces, where all bipartite states are entangled.

Two-photon states are essential for quantum technologies such as metrology, lithography, and communication. One of the primary methods of two-photon generation is based on parametric down-conversion, but this suffers from low efficiency and a large footprint. This work is a detailed investigation of an alternative approach: two-photon generation from an emitter in a doubly resonant cavity. The system is modeled by the Lindblad Master Equation, and an approximate analytical solution is derived to determine the practically achievable limits on efficiency and brightness. Additionally, the optimal cavity parameters for achieving these limits are also identified. For experimentally feasible parameters, the maximum efficiency is approximately $35\%$, which is several times larger than that of parametric down-conversion-based methods. The optimal rate and efficiency for two-photon generation are achieved when the outcoupling rate of the cavity mode at the two-photon emission frequency matches the single-photon atom-field coupling strength. Moreover, the outcoupling rate of the cavity mode at the one-photon emission frequency for single photons should be minimized. The cavity field properties are also examined by studying the second-order correlation function at zero time delay and the Mandel Q parameter, revealing highly bunched two-photon emission and super-Poissonian statistics. The quantum-jump framework, combined with Monte Carlo simulations, is used to characterize the mechanism of two-photon emission and the emission spectra of the cavity. Two-photon emission is demonstrated to be a rapid cascade process of quantum jumps, and its spectrum consists of three prominent peaks corresponding to transitions between the dressed states of the system.

(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators. This is always the case with a continuous onsite symmetry or with a local energy conservation law. (ii) We explain a simple algorithm for a formulation of the shallow unitary circuit learning problem and relate it to an open question on strictly locality-preserving unitaries (quantum cellular automata). (iii) We show that any translation-invariant quantum cellular automaton in $D$-dimensional lattice of volume $V$ can be implemented using only $O(V)$ local gates in a staircase fashion using invertible subalgebra pumping.

The high complexity of many-body quantum dynamics means that essentially all approaches either exploit special structure or are approximate in nature. One such approach--the memory function formalism--involves a carefully chosen split into fast and slow modes. An approximate model for the fast modes can then be used to solve for Green's functions $G(z)$ of the slow modes. Using a formulation in operator Krylov space known as the recursion method, we prove the emergence of a universal random matrix description of the fast mode dynamics. This is captured by the level-$n$ Green's function $G_n (z)$, which we show approaches universal scaling forms in the fast limit $n\to\infty$. Notably, this emergent universality can occur in both chaotic and non-chaotic systems, provided their spectral functions are smooth. This universality of $G_n (z)$ is precisely analogous to the universality of eigenvalue correlations in random matrix theory (RMT), even though there is no explicit randomness present in the Hamiltonian. At finite $z$ we show that $G_n (z)$ approaches the Wigner semicircle law, while if $G(z)$ is the Green's function of certain hydrodynamical variables, we show that at low frequencies $G_n (z)$ is instead governed by the Bessel universality class from RMT. As an application of this universality, we give a numerical method--the spectral bootstrap--for approximating spectral functions from Lanczos coefficients. Our proof involves a map to a Riemann-Hilbert problem which we solve using a steepest-descent-type method, rigorously controlled in the $n\to\infty$ limit. We are led via steepest-descent to a Coulomb gas optimization problem, and we discuss how a recent conjecture--the `Operator Growth Hypothesis--is linked to a confinement transition in this Coulomb gas. These results elevate the recursion method to a theoretically principled framework with universal content.

Floquet code is a dynamical quantum memory with a periodically evolving logical space. As a defining feature, the code exhibits an anyon automorphism after each period, giving rise to a non-trivial evolution of each logical state. In this paper, we study the Floquet code under local decoherence and perfect measurements and demonstrate that below the decoherence threshold, the code is in a robust phase characterized by the anyon automorphism. We first derive the 3D statistical mechanics model for the maximum likelihood decoder of the 2D Floquet code under local Pauli decoherence. We identify a class of two-qubit Pauli channels under which the 3D statistical mechanics model becomes decoupled 2D models and obtain the threshold for such decoherence channels. We then propose a diagnostic of the anyon automorphism in the presence of local decoherence. We analytically show that this diagnostic distinguishes the Floquet code from the toric code under repeated syndrome measurements and undergoes a phase transition at the threshold.

We prove formulas for the multi-instanton corrections to the overlap and energies of a 1D same-level asymmetric double well using the Euclidean path integral. Both the odd and even instanton sectors are summed to all orders. The double well is same-level asymmetric in the sense that the potentials at neighboring wells have the same bottom level but can have different Hessians/curvatures/frequencies, which modify Coleman's original formulas. This for instance implies that the reference model used to calculate the functional determinant of quantum fluctuations must now interpolate between simple harmonic oscillators of different frequencies. Examples of symmetric double and triple wells are worked out.

Quantum non-Gaussian states of traveling light fields are crucial components of quantum information processing protocols; however, their preparation is experimentally challenging. In this paper, we discuss the minimal requirements imposed on the quantum efficiency of photon number resolving detectors and the quality of the squeezing operation in an experimental realization of certifiable quantum non-Gaussian states of individual photonic states with three, four, and five photons.

Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers. However, choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task. Quantum Architecture Search (QAS) algorithms enable automatic generation of quantum circuits tailored to the provided problem. Existing QAS approaches typically adapt classical neural architecture search techniques, training machine learning models to sample relevant circuits, but often overlook the inherent quantum nature of the circuits they produce. By reformulating QAS from a quantum perspective, we propose a sampling-free differentiable QAS algorithm that models the search process as the evolution of a quantum mixed state, which emerges from the search space of quantum circuits. The mixed state formulation also enables our method to incorporate generic noise models, for example the depolarizing channel, which cannot be modeled by state vector simulation. We validate our method by finding circuits for state initialization and Hamiltonian optimization tasks, namely the variational quantum eigensolver and the unweighted max-cut problems. We show our approach to be comparable to, if not outperform, existing QAS techniques while requiring significantly fewer quantum simulations during training, and also show improved robustness levels to noise.

Identify, Transform, Benchmark, Show Quantum Advantage (ITBQ): Evaluating use cases for quantum computers. We introduce a four-step framework for assessing quantum computing applications -- from identifying relevant industry problems to demonstrating quantum advantage -- addressing steps often overlooked in the literature, such as rigorous benchmarking against classical solutions and the challenge of translating real-world tasks onto quantum hardware. Applying this framework to cases like NMR, multireference chemistry, and radicals reveals both significant opportunities and key barriers on the path to practical advantage. Our results highlight the need for transparent, structured criteria to focus research, guide investment, and accelerate meaningful quantum progress.

Page's seminal result on the average von Neumann (VN) entropy does not immediately apply to realistic many-body systems which are restricted to physically relevant smaller subspaces. We investigate here the VN entropy averaged over the pure states in the subspace $\mathcal{H}_E$ corresponding to a narrow energy shell centered at energy $E$. We find that the average entropy is $\overline{S}_{1} \simeq \ln d_1$, where $d_1$ represents first subsystem's effective number of states relevant to the energy scale $E$. If $d_E = \dim{(\mathcal{H}_E)}$ and $D$ ($D_1$) is the Hilbert space dimension of the full system (first subsystem), we estimate that $d_1 \simeq D_1^\gamma$, where $\gamma = \ln (d_E) / \ln (D)$ for nonintegrable (chaotic) systems and $\gamma < \ln (d_E) / \ln (D)$ for integrable systems. This result can be reinterpreted as a volume-law of entropy, where the volume-law coefficient depends on the density-of-states for nonintegrable systems, and remains below the maximal possible value for integrable systems. We numerically analyze a spin model to substantiate our main results.

Optically active spin defects in van der Waals (vdW) materials have recently emerged as versatile quantum sensors, enabling applications from nanoscale magnetic field detection to the exploration of novel quantum phenomena in condensed matter systems. Their ease of exfoliation and compatibility with device integration make them promising candidates for future quantum technologies. Here we report the observation and room-temperature coherent control of spin defects in the high-temperature crystalline phase of germanium disulfide ($\beta$-GeS2), a two-dimensional (2D) semiconductor with low nuclear spin density. The observed spin defects exhibit spin-1/2 behavior, and their spin dynamics can be explained by a weakly coupled spin-pair model. We implement dynamical decoupling techniques to extend the spin coherence time (T$_2$) by a factor of 20. Finally, we use density functional theory (DFT) calculations to estimate the structure and spin densities of two possible spin defect candidates. This work will help expand the field of quantum sensing with spin defects in van der Waals materials.

We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian noise in the equation of motion and in the initial conditions. Our algorithm can approximate the expected value of any correlation function that depends on $O(1)$ variables with rigorous bounds on the approximation error. The runtime scales polynomially with $\log{N}$, $t$, $J$, and $\lambda_1^{-1}$, where $N$ is the total number of variables, $t$ is the evolution time, $J$ is the nonlinearity strength, and $\lambda_1$ is the smallest dissipation rate. However, the runtime scales exponentially with a parameter quantifying inverse relative error in the initial conditions. To the best of our knowledge, this is the first rigorous quantum algorithm capable of simulating strongly nonlinear systems with $J\gg \lambda_1$ at the cost poly-logarithmic in $N$ and polynomial in $t$. The considered simulation problem is shown to be BQP-complete, providing a strong evidence for a quantum advantage. We benchmark the quantum algorithm via numerical experiments by simulating a vortex flow in the 2D Navier Stokes equation.

We study the interactions mediated by symmetric superconducting quantum interference device (SQUID), their renormalizations, and applicability of the anharmonic oscillator model for a coupled phase qubit. The coupling SQUID can switch between single- or two-photon interaction in situ. We consider a coupled resonator and an rf SQUID. The latter dwells in the vicinity of its metastable well holding a number of anharmonic energy states and acts as an artificial atom known as the phase qubit. Apart from the linear and two-photon couplings, interactions of optomechanical type and a cross-Kerr coupling arise. Near the two-photon resonance, we calculate the renormalizations due to nonresonant interactions, which are more prominent with the higher Josephson energy of the coupler. We interpret the renormalizations by depicting some of the virtual processes involved. That also allows us to determine the minimal amount of metastable states in the phase qubit for the renormalization formulas to hold.

Quantum emitters in hexagonal boron nitride (hBN) have gained significant attention due to a wide range of defects that offer high quantum efficiency and single-photon purity at room temperature. Most theoretical studies on hBN defects simulate monolayers, as this is computationally cheaper than calculating bulk structures. However, most experimental studies are carried out on multilayer to bulk hBN, which creates additional possibilities for discrepancies between theory and experiment. In this work, we present an extended database of hBN defects that includes a comprehensive set of bulk hBN defects along with their excited-state photophysical properties. The database features over 120 neutral defects, systematically evaluated across charge states ranging from -2 to 2 (600 defects in total). For each defect, the most stable charge and spin configurations are identified and used to compute the zero-phonon line, photoluminescence spectrum, absorption spectrum, Huang-Rhys (HR) factor, interactive radiative lifetimes, transition dipole moments, and polarization characteristics. Our analysis reveals that the electron-phonon coupling strength is primarily influenced by the presence of vacancies, which tend to induce stronger lattice distortions and broaden phonon sidebands. Additionally, correlation analysis shows that while most properties are independent, the HR factor strongly correlates with the configuration coordinates. All data are publicly available at this https URL, along with a new application programming interface (API) to facilitate integration with machine learning workflows. This database is therefore designed to bridge the gap between theory and experiment, aid in the reliable identification of quantum emitters, and support the development of machine-learning-driven approaches in quantum materials research.

We construct several explicit instances of quantum Tanner codes, a class of asymptotically good quantum low-density parity check (qLDPC) codes. The codes are constructed using dihedral groups and random pairs of classical codes and exhibit high encoding rates, relative distances, and pseudo-thresholds. Using the BP+OSD decoder, we demonstrate good performance in the phenomenological and circuit-level noise settings, comparable to the surface code with similar distances. Finally, we conduct an analysis of the space-time overhead incurred by these codes.

Quantum-state texture is a newly recognized quantum resource that has garnered attention with the advancement of quantum theory. In this work, we address several key aspects of quantum-state texture resource theory, including the quantification of quantum-state texture, quantum state transformation under free operations, and the relationships between quantum resources. We first propose two new measures of quantum-state texture and introduce a specific functional form for constructing such measures via the convex roof method. Then, we determine the maximum probability of quantum state transformation under free operations. Finally, we establish connections between quantum-state texture and other prominent quantum resources, such as coherence, imaginarity, and predictability. Our research contributes to the measure theory of quantum-state texture and enriches the overall framework of quantum-state texture resource theory.

Group-IV vacancy (G4V, or XV, where X = Si, Ge, Sn, Pb) color centers constitute a novel and promising class of defects in diamonds. This chapter reviews and refines the theoretical models for the XV systems, encompassing the intrinsic interactions, including spin-orbit coupling and electron-phonon interactions, and the external interactions involving strain, electric, light, and magnetic fields. Based on the refined model, we predict their properties, explain the experimental data, and suggest follow-up experiments. This article established a solid foundation for controlling the XV system, thus paving the way for quantum information processing.

A central challenge in quantum resource theory is to provide operational meaning to quantum resources that offer distinct advantages over the convex set of resource-free states in specific physical tasks. We propose a novel framework to define the resource deficiency of a given state relative to the set of maximal resource states in physical tasks. The proposed geometric measure satisfies this framework's conditions for both quantum coherence and entanglement, and it precisely quantifies the minimal disadvantage of a given state compared to maximal resource states in subchannel discrimination under certain conditions. These extensions and new interpretations broaden the scope of quantum resource theories and provide more comprehensive operational interpretations.

Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits. Building on our recent work on adaptive and windowed phase-estimation methods, we have developed a modular, windowed formulation of Shor's algorithm that mitigates these limitations by restructuring phase estimation into shallow, independent circuit blocks that can be executed sequentially or in parallel, followed by lightweight classical postprocessing. This approach allows for a reduction in the size of the phase (or counting) register from a large number of qubits down to a small, fixed block size of only a few qubits (for example, three or four phase qubits were sufficient for the computational examples considered in this work), while leaving the work register requirement unchanged. The independence of the blocks allows for parallel execution and makes the approach more compatible with near-term hardware than the standard Shor's formulation. An additional feature of the framework is the overlap mechanism, which introduces redundancy between blocks and enables robust reconstruction of phase information, though zero-overlap configurations can also succeed in certain regimes. Numerical simulations verify the correctness of the modular formulation while also showing substantial reductions in counting qubits per block.

We introduce a certified pruning framework that consolidates the principles of counterfactual consistency and their networked extensions into a single operational model, with consequences for both quantum foundations and cryptographic hardness. First, we formalize epsilon-counterfactual instrumentation and epsilon-stability, capturing noisy but testable constraints in laboratory contextuality experiments. Second, we extend these constraints to networks of contexts, yielding contextuality-type inequalities that apply globally across a CNF-SAT instance. Third, we implement a propagate-and-prune solver in which every learned clause is certified by a dual Farkas certificate verified in exact arithmetic. This guarantees soundness while enabling sub-exponential pruning: if the induced network provides a per-variable pruning rate rho in (0,1) under epsilon-stable propagation, the search runs in time (2-rho)^n. These bounds do not contradict ETH or SETH: the worst case remains exponential, but structured families admit provable speedups. In cryptography, the results highlight how such reductions could affect hardness margins in idealized primitives; in foundations, they motivate laboratory tests of counterfactual bounds as potential probes of computational complexity. We explicitly distinguish experimental epsilon, which quantifies laboratory visibility, from numerical epsilon, which is a solver tolerance. This builds directly on our earlier framework for epsilon-instrumentation, here integrated into certified pruning with dual certificates.

Shannon-Renyi and stabilizer entropies are key diagnostics of structure, non-stabilizerness, phase transitions, and universality in quantum many-body states. We establish an exact correspondence for quadratic fermions: for any nondegenerate Gaussian eigenstate, the stabilizer Renyi entropy equals the Shannon-Renyi entropy of a number-conserving free-fermion eigenstate on a doubled system, evaluated in the computational basis. Specializing to the transverse-field Ising (TFI) chain, the TFI ground state stabilizer entropies maps to the Shannon-Renyi entropies of the XX-chain ground state of length $2L$. Building on this correspondence, together with other exact identities we prove, closed expressions for the stabilizer entropy at indices $\alpha=\frac{1}{2},2,4$ for a broad class of critical closed free-fermion systems were derived. Each of these can be written with respect to the universal functions of the TFI chain. We further obtain conformal-field-theory scaling laws for the stabilizer entropy under both periodic and open boundaries at arbitrary Renyi index for these critical systems.

Monitored dynamics in quantum circuits provide tunable platforms for the realization of novel non-equilibrium phases. Motivated by recent advances in monitored Kitaev circuits, we investigate the monitored dynamics of the qudit ($d=4$) generalizations of the Kitaev model on the honeycomb and square lattices. In the absence of additional perturbations, the measurement-only dynamics of these models map onto multi-flavor loop models and display either critical or area-law entanglement scaling. Magnetic field terms couple different flavors and when measured with sufficiently large probability, they enhance the stability of the area-law phase that hosts the logical qubits. In a circuit picture, these terms correspond to single-qubit measurements and can be interpreted as errors. We also examine the impact of two-qubit measurements that commute with the plaquette operator, which induce effective non-quadratic interactions between Majorana fermions. These interactions can drive a transition to a volume-law-entangled phase and, for sufficiently strong coupling, stabilize a distinct area-law phase with an additional logical qubit for the square lattice model. Our results reveal a rich interplay between quantum spin liquids and monitored circuit dynamics, highlighting new mechanisms for engineering and controlling entanglement phases in multi-flavor Majorana systems.

This paper investigates the emergence of classical objectivity in quantum systems through the measure of Functional Information in Quantum Darwinism ($FI_{QD}$). The goal is to quantify objectivity as the abundance of environment fragments that independently contain sufficient information about a system's pointer states. The method relies on the Holevo quantity -- an upper bound on accessible information -- and introduces a tolerance criterion called $\delta$-adequacy, where fragments are considered adequate if they retain at least $(1-\delta)H_S$ bits of pointer information. Numerical simulations of a dephasing model with fragment sampling reveal three robust features: (i) an early-time regime where $\log R_\delta(t)$ grows approximately linearly, (ii) capacity-limited plateaus determined by fragment size and environment dimension, and (iii) stability of the onset criterion under different sampling strategies and overlap corrections. These results establish $FI_{QD}$ as a practical and conservative yardstick for operational objectivity. Beyond numerical findings, the analysis links redundancy growth to thermodynamic costs of record formation and interprets $FI_{QD}$ as a resource monotone under noisy dynamics. The study suggests that classical objectivity emerges not as an assumption but as a quantifiable, resource-limited abundance of redundant records.

Quantum computing promises significant speed-ups for certain algorithms but the practical use of current noisy intermediate-scale quantum (NISQ) era computers remains limited by resources constraints (e.g., noise, qubits, gates, and circuit depth). Quantum circuit optimization is a key mitigation strategy. In this context, ZX-calculus has emerged as an alternative framework that allows for semantics-preserving quantum circuit optimization. We review ZX-based optimization of quantum circuits, categorizing them by optimization techniques, target metrics and intended quantum computing architecture. In addition, we outline critical challenges and future research directions, such as multi-objective optimization, scalable algorithms, and enhanced circuit extraction methods. This survey is valuable for researchers in both combinatorial optimization and quantum computing. For researchers in combinatorial optimization, we provide the background to understand a new challenging combinatorial problem: ZX-based quantum circuit optimization. For researchers in quantum computing, we classify and explain existing circuit optimization techniques.

The Mpemba effect is the phenomenon whereby systems farther from equilibrium may relax faster. In this work, we show that this counterintuitive behavior appears in the very measures that define quantum complexity. Using the framework of quantum resource theories, we study the dynamics of coherence, imaginarity, non-Gaussianity, and magic state resources in random circuit models. Our results reveal that coherence and imaginarity display a quantum Mpemba effect when the system is initialized in resourceful product states, while non-Gaussianity and magic do not. Strikingly, all four resources exhibit the so-called Pontus-Mpemba effect: an initial "preheating" stage accelerates relaxation compared to direct "cooling" dynamics. Taken together, our findings show that Mpemba physics extends beyond thermodynamics and asymmetry, emerging broadly in the resource theories that capture aspects of quantum complexity.

We experimentally demonstrate efficient interfacing of a large number of atoms to an optical nanofiber using an optical lattice with tunable spacing ($0.88-1.5~\mu$m) projected onto the nanofiber. The lattice beam and reflections from the nanofiber yield trap potentials that provide tight confinement in all motional degrees of freedom $\approx 220$ nm above the nanofiber surface, enabling efficient atom-photon coupling. We achieve trapping of $\approx1300$ atoms in periodic trap sites with a trap lifetime of $\approx15$ ms. We also observe the effect of varied lattice periods on the atomic motional frequencies. Our new scheme is adaptable to other nanophotonic cold-atom systems and provides a versatile and scalable platform for studying photon-mediated long-range collective interactions.

We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum mechanics. As established by Wigner, all quantum symmetries must be represented by either unitary or antiunitary transformations. Relinquishing an implicit assumption of invertibility, we demonstrate that the fundamental invariance of quantum transition probabilities under the application of symmetries mandates that all non-invertible symmetries may only correspond to {\it projective} unitary or antiunitary transformations, i.e., {\it partial isometries}. This extends the notion of physical states beyond conventional rays in Hilbert space to equivalence classes in an {\it extended, gauged Hilbert space}, thereby broadening the traditional understanding of symmetry transformations in quantum theory. We discuss consequences of this result and explicitly illustrate how, in simple model systems, whether symmetries be invertible or non-invertible may be inextricably related to the particular boundary conditions that are being used.

Quantum random access memories (QRAMs) are pivotal for data-intensive quantum algorithms, but existing general-purpose and domain-specific architectures are hampered by a critical bottleneck: a heavy reliance on non-Clifford gates (e.g., T-gates), which are prohibitively expensive to implement fault-tolerantly. To address this challenge, we introduce the Stabilizer-QRAM (Stab-QRAM), a domain-specific architecture tailored for data with an affine Boolean structure ($f(\mathbf{x}) = A\mathbf{x} + \mathbf{b}$ over $\mathbb{F}_2$), a class of functions vital for optimization, time-series analysis, and quantum linear systems algorithms. We demonstrate that the gate interactions required to implement the matrix $A$ form a bipartite graph. By applying König's edge-coloring theorem to this graph, we prove that Stab-QRAM achieves an optimal logical circuit depth of $O(\log N)$ for $N$ data items, matching its $O(\log N)$ space complexity. Critically, the Stab-QRAM is constructed exclusively from Clifford gates (CNOT and X), resulting in a zero $T$-count. This design completely circumvents the non-Clifford bottleneck, eliminating the need for costly magic state distillation and making it exceptionally suited for early fault-tolerant quantum computing platforms. We highlight Stab-QRAM's utility as a resource-efficient oracle for applications in discrete dynamical systems, and as a core component in Quantum Linear Systems Algorithms, providing a practical pathway for executing data-intensive tasks on emerging quantum hardware.

We propose some new uses of toric variety structures in the study of quantum computation for various radices.

Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can derive a quantum generalization of the Fisher information matrix in a natural way as the Hessian matrix arising in a Taylor expansion of a smooth divergence. Such an approach is appealing for quantum information theorists, given the ubiquity of divergences in quantum information theory. In contrast to the classical case, there is not a unique quantum generalization of the Fisher information matrix, similar to how there is not a unique quantum generalization of the relative entropy or the Rényi relative entropy. In this paper, I derive information matrices arising from the log-Euclidean, $\alpha$-$z$, and geometric Rényi relative entropies, with the main technical tool for doing so being the method of divided differences for calculating matrix derivatives. Interestingly, for all non-negative values of the Rényi parameter $\alpha$, the log-Euclidean Rényi relative entropy leads to the Kubo-Mori information matrix, and the geometric Rényi relative entropy leads to the right-logarithmic derivative Fisher information matrix. Thus, the resulting information matrices obey the data-processing inequality for all non-negative values of the Rényi parameter $\alpha$ even though the original quantities do not. Additionally, I derive and establish basic properties of $\alpha$-$z$ information matrices resulting from the $\alpha$-$z$ Rényi relative entropies. For parameterized thermal states and time-evolved states, I establish formulas for their $\alpha$-$z$ information matrices and hybrid quantum-classical algorithms for estimating them, with applications in quantum Boltzmann machine learning.

We show that a basic quantum white noise process formally reproduces quantum stochastic calculus when the appropriate normal / chronological orderings are prescribed. By normal ordering techniques for integral equations and a generalization of the Araki-Woods representation, we derive the master and random Heisenberg equations for an arbitrary Gaussian state: this includes thermal and squeezed states.

Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase the key idea of Maxwell and Boltzmann, the Stoßzahlansatz, a far more general, abstract ansatz is developed. An increase of the Gibbs-Shannon-von Neumann entropy results without the usual coarse-graining. The mathematical structure of the ansatz also provides avenues for efficient computation and simulation.

In a relativistic framework, it is generally accepted that quantum steering of maximally entangled states provide greater advantages in practical applications compared to non-maximally entangled states. In this paper, we investigate quantum steering for four different types of Bell-like states of fermionic modes near the event horizon of a Schwarzschild black hole. In some parameter spaces, the peak of steering asymmetry corresponds to a transition from two-way to one-way steerability for Bell-like states under the influence of the Hawking effect. It is intriguing to find that the fermionic steerability of the maximally entangled states experiences sudden death with the Hawking temperature, while the fermionic steerability of the non-maximally entangled states maintains indefinite persistence at infinite Hawking temperature. In contrast to prior research, this finding suggests that quantum steering of non-maximally entangled states is more advantageous than that of maximally entangled states for processing quantum tasks in the gravitational background. This surprising result overturns the traditional idea of ``the advantage of maximally entangled steering in the relativistic framework" and provides a new perspective for understanding the Hawking effect of the black hole.

Strong light-matter interactions can create non-equilibrium materials with on-demand novel functionalities. For periodically driven solids, the Floquet theorem provides the natural states to characterize the physical properties of these laser-dressed systems. However, signatures of the Floquet states are needed, as common experimental conditions, such as pulsed laser excitation and dissipative many-body dynamics, can disrupt their formation and survival. Here, we identify a tell-tale signature of Floquet states in the linear optical response of laser-dressed solids that remains prominent even in the presence of strong spectral congestion of bulk matter. To do so, we introduce a computationally efficient strategy based on the Floquet formalism to finally capture the full frequency-dependence in the optical response properties of realistic laser-dressed crystals, and use it investigate the Floquet engineering in a first-principle model for ZnO of full dimensionality. The computations reveal intense, spectrally isolated, laser-controllable, absorption/stimulated emission features at mid-infrared energies present for a wide range of laser-driving conditions that arise due to the hybridization of the Floquet states. As such, these spectral features open a purely optical pathway to investigate the birth and survival of Floquet states while avoiding the experimental challenges of fully reconstructing the band structure.

Scaling full finetuning of large foundation models strains GPU memory and training time. Parameter Efficient Fine-Tuning (PEFT) methods address this issue via adapter modules which update only a small subset of model parameters. In this work, we introduce Quantum-Inspired Compound Adapters (QuIC Adapters), a PEFT approach inspired from Hamming-weight preserving quantum circuits that can effectively finetune a model using less than 0.02\% memory footprint of the base model. QuIC adapters preserve pretrained representations by enforcing orthogonality in weight parameters, and have native deployment mechanisms on quantum computers. We test QuIC adapters by finetuning large language models like LLaMA and vision transformers on language, math, reasoning and vision benchmarks. In its first-order configuration, QuIC recovers the performance of existing orthogonal methods, while higher-order configurations enable substantial parameter compression (over 40x smaller than LoRA) for a modest performance trade-off, unlocking applications in highly resource-constrained environments. Through ablation studies, we determine that combining multiple Hamming-weight orders with orthogonality and matrix compounding are essential for performant finetuning. Our findings suggest that QuIC adapters offers a promising direction for efficient finetuning of foundation models in resource-constrained environments.

Recently, thanks to the development of artificial intelligence (AI) there is increasing scientific attention in establishing the connections between theoretical physics and AI. Traditionally, these connections have been focusing mostly on the relation between string theory and image processing and involve important theoretical paradigms such as holography. Recently G. Bianconi has formulated the Gravity from Entropy (GfE) approach to quantum gravity in which gravity is derived from the geometric quantum relative entropy (GQRE) between two metrics associated with the Lorentzian spacetime. Here it is demonstrated that the famous Perona-Malik algorithm for image processing is the gradient flow that maximizes the GfE action in its simple warm-up scenario. Specifically, this algorithm is the outcome of the maximization of the GfE action calculated between two Euclidean metrics: the one of the support of the image and the one induced by the image. As the Perona-Malik algorithm is known to preserve sharp contours, this implies that the GfE action, does not in general lead to uniform images upon iteration of the gradient flow dynamics as it would be intuitively expected from entropic actions maximising classical entropies. Rather, the outcome of the maximization of the GfE action is compatible with the preservation of complex structures. These results provide the geometrical and information theory foundations for the Perona-Malik algorithm and might contribute to establish deeper connections between GfE, machine learning and brain research.

Optical lattice clocks (OLCs) are at the forefront of precision metrology, operating near a standard quantum limit (SQL) set by quantum noise. Harnessing quantum entanglement offers a promising route to surpass this limit, yet there remain practical roadblocks concerning scalability and measurement resolution requirements. Here, we adapt the holonomic quantum-gate concept to develop a novel Rabi-type "global-phase spectroscopy" (GPS) that utilizes the detuning-sensitive global Aharanov-Anandan phase. With this approach, we are able to demonstrate quantum-amplified time-reversal spectroscopy in an OLC that achieves 2.4(7) dB metrological gain without subtracting the laser noise, and 4.0(8) dB improvement in laser noise sensitivity beyond the SQL. We further introduce rotary echo to protect the dynamics from inhomogeneities in light-atom coupling and implement a laser-noise-canceling differential measurement through symmetric phase encoding in two nuclear spin states. Our technique is not limited by measurement resolution, scales easily owing to the global nature of entangling interaction, and exhibits high resilience to typical experimental imperfections. We expect it to be broadly applicable to next-generation atomic clocks and other quantum sensors approaching the fundamental quantum precision limits.

Quantum-logic spectroscopy has become an increasingly important tool for the state detection and readout of trapped atomic and molecular ions which do not possess easily accessible closed-cycling optical transitions. In this approach, the internal state of the target ion is mapped onto a co-trapped auxiliary ion. This mapping is typically mediated by normal modes of motion of the two-ion Coulomb crystal in the trap. The present study investigates the role of spectator modes not directly involved in a measurement protocol relying on a state-dependent optical-dipole force. We identify a Debye-Waller-type effect that modifies the response of the two-ion string to the force. We show that cooling the spectator modes of the string allows for the detection of the rovibrational ground state of an N$_2^+$ molecular ion with a computed statistical fidelity exceeding 99.99%, improving on previous experiments by more than an order of magnitude while also halving the experimental time. This enhanced sensitivity enables the simultaneous identification of multiple rotational states with markedly weaker signals.

An introduction to Bose-Einstein condensation and the $\lambda$-transition is given. Results of quantum loop Monte Carlo simulations are presented for interacting Lennard-Jones helium-4. The optimum condensation fraction is found by minimizing the constrained free energy. The results show that approaching the transition the growth of pure position permutation loops and the consequent divergence of the heat capacity are enabled by the suppression of condensation and consequently of superfluidity. Condensation and superfluidity emerge at the peak of the heat capacity due to mixed position permutation chains.

Donor-acceptor pairs (DAPs) in wide-bandgap semiconductors are promising platforms for the realization of quantum technologies, due to their optically controllable, long-range dipolar interactions. Specifically, Al-N DAPs in bulk silicon carbide (SiC) have been predicted to enable coherent coupling over distances exceeding 10 nm. However, their practical implementations require an understanding of the properties of these pairs near surfaces and interfaces. Here, using first principles calculations we investigate how the presence of surfaces influence the stability and optical properties of Al-N DAPs in SiC, and we show that they retain favorable optical properties comparable to their bulk counterparts, despite a slight increase in electron-phonon coupling. Furthermore, we introduce the concept of surface-defect pairs (SDPs), where an electron-hole pair is generated between a near-surface defect and an occupied surface state located in the bandgap of the material. We show that vanadium-based SDPs near OH-terminated 4H-SiC surfaces exhibit dipoles naturally aligned perpendicular to the surface, greatly enhancing dipole-dipole coupling between SDPs. Our results also reveal significant polarization-dependent modulation in the stimulated emission and photoionization cross sections of V-based SDPs, which are tunable by two orders of magnitude via the polarization angle of the incident laser light. The near-surface defects investigated here provide novel possibilities for the development of hybrid quantum-classical interfaces, as they can be used to mediate information transfer between quantum nodes and integrated photonic circuits.

Floquet engineering of electronic states by light is a central topic in modern experiments. However, the impact of many-body interactions on the single-electron properties remains unclear in this non-equilibrium situation. We propose that interaction effects could be reasonably understood by performing perturbative expansion in both the pump field and the electron-electron interaction when computing physical quantities. As an example, we apply this approach to semiconductors and show analytically that excitonic effects, i.e., effects of electron-hole interaction, lead to dramatic corrections to the single-electron Floquet spectra even when the excitons are only virtually excited by the pump light. We compute these effects in phosphorene and monolayer MoS$_2$ for time- and angle-resolved photoemission spectroscopy and ultrafast optical experiments.

We show that an effective gravitational field naturally emerges in quantum materials with long-wavelength spin (or pseudospin) textures. When the itinerant electrons' spin strongly couples to the background spin texture, it effectively behaves as a spinless particle in a curved space, with the curvature arising from quantum corrections to the electron's spin orientation. The emergent curved space gives rise to the electron lensing effect, an analog of the gravitational lensing. The lensing effect can appear in systems without (emergent) magnetic fields, such as those with coplanar spin textures. Our work shows that novel ``gravitational'' phenomena generically appear in quantum systems due to nonadiabaticity, opening new research directions in quantum physics.

The false vacuum decay rate is of important meaning in understanding the Universe, such as the symmetry breaking process in the early universe and the age of our universe, which is conventionally calculated with the saddle-point approximation in the field theory. Utilizing the extension of the Wigner function in quantum field theory, we numerically calculate the decay rate of the false vacuum through path integral. We study the decay rate for the thermal fluctuation scenarios and its dependence on the potential shape, and found that the false vacuum decay occurs following an exponentially decay rate, and the speed of vacuum decay decreases when the initial energy of the system decreases and the potential height increase. The discrepancy between the simulation results and the theoretical prediction of finite temperature effective field theory is observed.

Accurate and efficient simulation of nonadiabatic dynamics is highly desirable for understanding charge and energy transfer in complex systems. A key criterion for obtaining an accurate method is conservation of the Quantum Boltzmann Distribution (QBD). For a single surface, Matsubara dynamics is known to conserve the QBD, as a consequence of truncating the dynamics in the higher normal modes of the imaginary-time path integral. Recently, a nonadiabatic Matsubara (NA-Mats) dynamics has been proposed (J. Chem. Phys., 2021, 154, 124124) which truncates in the normal modes of the nuclear variables but not in the electronic variables, which are described with the Meyer-Miller-Stock-Thoss (MMST) representation. Surprisingly, this NA-Mats method does not appear to conserve the QBD for a general system. This poses the question of the effect of truncating the higher path integral normal modes of the electronic variables in the MMST representation. In this article, we present what we believe is the first study of electronic normal modes of the MMST representation. We find that observables are not usually a function of a finite number of normal modes and that the higher normal modes are not constrained by the distribution, unlike in conventional nuclear normal modes. Furthermore, truncating the dynamics in MMST normal modes leads to inaccurate correlation functions and while the QBD appears conserved for an ensemble of trajectories, it is not for a single trajectory. Overall, this suggests that MMST path integral normal modes are not optimal for obtaining an accurate, QBD conserving nonadiabatic dynamics method.

Recent advances in machine learning (ML) have accelerated progress in calibrating and operating quantum dot (QD) devices. However, most ML approaches rely on access to large, representative datasets designed to capture the full spectrum of data quality encountered in practice, with both high- and low-quality data for training, benchmarking, and validation, with labels capturing key features of the device state. Collating such datasets experimentally is challenging due to limited data availability, slow measurement bandwidths, and the labor-intensive nature of labeling. QDFlow is an open-source physics simulator for multi-QD arrays that generates realistic synthetic data with ground-truth labels. QDFlow combines a self-consistent Thomas-Fermi solver, a dynamic capacitance model, and flexible noise modules to simulate charge stability diagrams and ray-based data closely resembling experiments. With an extensive set of parameters that can be varied and customizable noise models, QDFlow supports the creation of large, diverse datasets for ML development, benchmarking, and quantum device research.

We study methods for efficient preparation of approximate ground states of $SU(3)$ lattice gauge theory on quantum hardware. Working in a variant of the electric basis, we introduce a refinement of the irrep truncation based on the energy density of site singlets, which provides a finer gradation of simulation complexity. Using strong-coupling perturbation theory as a guide, we develop simple ansatz circuits for ground state preparation and test them via classical simulation on small lattices, including the $2\times 2$ plaquette lattice in $d=2$ and the cube in $d=3$. We contrast state fidelities and resource requirements of variational methods against adiabatic state preparation and introduce a method that hybridizes the two approaches. Finally, we report on the public release of \texttt{ymcirc} -- a package of tools for building $SU(3)$ circuits and processing measurements -- and \texttt{pyclebsch}, a package for efficiently computing $SU(N)$ Clebsch-Gordan coefficients.