Quantum networks (QNs) supported by terahertz (THz) wireless links present a transformative alternative to fiber-based infrastructures, particularly in mobile and infrastructure-scarce environments. However, signal attenuation, molecular absorption, and severe propagation losses in THz channels pose significant challenges to reliable quantum state transmission and entanglement distribution. To overcome these limitations, we propose a dynamic reconfigurable intelligent surface (RIS)-assisted wireless QN architecture that leverages adaptive RIS elements capable of switching between active and passive modes based on the incident signal-to-noise ratio (SNR). These dynamic RIS elements enhance beamforming control over amplitude and phase, enabling robust redirection and compensation for THz-specific impairments. We develop a detailed analytical model that incorporates key physical layer phenomena in THz quantum links, including path loss, fading, thermal noise, and alignment variations. A secure optimization framework is formulated to jointly determine RIS placement and entanglement generation rate (EGR) allocation, while satisfying fidelity, security, and fairness constraints under diverse quality of service (QoS) demands. The model also includes an exploration of side-channel vulnerabilities arising from dynamic RIS switching patterns. Simulation results demonstrate that the proposed architecture yields up to 87\% fidelity enhancement and 65\% fairness improvement compared to static RIS baselines, while maintaining robustness under realistic THz channel conditions. These results underscore the promise of dynamic RIS technology in enabling scalable and adaptive quantum communications over wireless THz links.

We develop a fundamental framework for the quantum mechanics of stochastic systems (QMSS), showing that classical discrete stochastic processes emerge naturally as perturbations of the quantum harmonic oscillator (QHO). By constructing exact perturbation potentials that transform QHO eigenstates into stochastic representations, we demonstrate that canonical probability distributions, including Binomial, Negative Binomial, and Poisson, arise from specific modifications of the harmonic potential. Each stochastic system is governed by a Count Operator (N), with probabilities determined by squared amplitudes in a Born-rule-like manner. The framework introduces a complete operator algebra for moment generation and information-theoretic analysis, together with modular projection operators (R_M) that enable finite-dimensional approximations supported by rigorous uniform convergence theorems. This mathematical structure underpins True Uniform Random Number Generation (TURNG) [Kuang, Sci. Rep., 2025], eliminating the need for external whitening processes. Beyond randomness generation, the QMSS framework enables quantum probability engineering: the physical realization of classical distributions through designed quantum perturbations. These results demonstrate that stochastic systems are inherently quantum-mechanical in structure, bridging quantum dynamics, statistical physics, and experimental probability realization.

Until very recently, it was generally believed that the (approximate) 2-design property is strictly stronger than anti-concentration of random quantum circuits, mainly because it was shown that the latter anti-concentrate in logarithmic depth, while the former generally need linear depth circuits. This belief was disproven by recent results which show that so-called relative-error approximate unitary designs can in fact be generated in logarithmic depth, implying anti-concentration. Their result does however not apply to ordinary local random circuits, a gap which we close in this paper, at least for 2-designs. More precisely, we show that anti-concentration of local random quantum circuits already implies that they form relative-error approximate state 2-designs, making them equivalent properties for these ensembles. Our result holds more generally for any random circuit which is invariant under local (single-qubit) unitaries, independent of the architecture.

Just how fast does the brickwork circuit form an approximate 2-design? Is there any difference between anticoncentration and being a 2-design? Does geometry matter? How deep a circuit will I need in practice? We tell you everything you always wanted to know about second moments of random quantum circuits, but were too afraid to compute. Our answers generally take the form of numerical results for up to 50 qubits. Our first contribution is a strategy to determine explicitly the optimal experiment which distinguishes any given ensemble from the Haar measure. With this formula and some computational tricks, we are able to compute $t = 2$ multiplicative errors exactly out to modest system sizes. As expected, we see that most families of circuits form $\epsilon$-approximate $2$-designs in depth proportional to $\log n$. For the 1D brickwork, we work out the leading-order constants explicitly. For graphs, we find some exceptions which are much slower, proving that they require at least $\Omega(n^2)$ gates. This answers a question asked by ref. 1 in the negative. We explain these exceptional architectures in terms of connectedness. Based on this intuition we conjecture universal upper and lower bounds for graph-sampled circuit ensembles. For many architectures, the optimal experiment which determines the multiplicative error corresponds exactly to the collision probability (i.e. anticoncentration). However, we find that the star graph anticoncentrates much faster than it forms an $\epsilon$-approximate $2$-design. Finally, we show that one needs only ten to twenty layers to construct an approximate $2$-design for realistic parameter ranges. This is a large constant-factor improvement over previous constructions. The parallel complete-graph architecture is not quite the fastest scrambler, partially resolving a question raised by ref. 2.

We introduce the resource-theoretic free energy of a quantum channel as the maximal work extractable from the channel as its output equilibrates to a thermal state and its reference system remains locally intact. It is proportional to the relative entropy between the given channel and the absolutely thermal channel. It attains a clear operational meaning as twice the asymptotic rates of athermality distillation and formation under Gibbs preserving superchannels, which map one absolutely thermal channel to another for a given bath, thereby revealing the asymptotic reversibility of the resource theory of athermality for quantum channels. Consequently, we establish that the optimal extractable work in converting one channel to another through the asymptotic athermality distillation and formation tasks equals the difference in their free energies. We call this optimal work the thermodynamic work capacity of channel conversion. Quantum information processing and computing fundamentally concern the manipulation and transformation of quantum channels, which encompass quantum states, their transformations, and measurements. A quantitative characterization of the optimal thermodynamic work gain or expenditure in quantum information processing constitutes a key step toward formulating thermodynamics of quantum processes.

In this paper, we compute the injective norm - a.k.a. geometric entanglement - of standard basis states of CSS quantum error-correcting codes. The injective norm of a quantum state is a measure of genuine multipartite entanglement. Computing this measure is generically NP-hard. However, it has been computed exactly in condensed-matter theory - notably in the context of topological phases - for the Kitaev code and its extensions, in works by Orús and collaborators. We extend these results to all CSS codes and thereby obtain the injective norm for a nontrivial, infinite family of quantum states. In doing so, we uncover an interesting connection to matroid theory and Edmonds' intersection theorem.

Harnessing topological effects offers a promising route to protect quantum states of light from imperfections, potentially enabling more robust platforms for quantum information processing. This capability is particularly relevant for active photonic circuits that generate quantum light directly on-chip. Here, we explore topological effects on photon-pair generation via spontaneous parametric down-conversion (SPDC) in nonlinear waveguide arrays, both theoretically and experimentally. A systematic comparison of homogeneous, trivial, and topological Su-Schrieffer-Heeger arrays reveals that only the topological configuration preserves a stable SPDC resonance spectrum under disorder in the tunnel couplings, with fluctuations in the resonance position reduced by more than one order of magnitude. An analytical model supports our experimental observations by linking this robustness to the band-structure properties of the interacting modes. These findings establish quadratic nonlinear waveguide arrays as a promising platform to explore the interplay of nonlinearity, topology, and disorder in quantum photonic circuits.

Decoders of quantum error correction (QEC) experiments make decisions based on detected errors and the expected rates of error events, which together comprise a detector error model. Here we show that the syndrome history of QEC experiments is sufficient to detect and estimate coherent errors, removing the need for prior device benchmarking experiments. Importantly, our method shows that experimentally determined detector error models work equally well for both stochastic and coherent noise regimes. We model fully-coherent or fully-stochastic noise for repetition and surface codes and for various phenomenological and circuit-level noise scenarios, by employing Majorana and Monte Carlo simulators. We capture the interference of coherent errors, which appears as enhanced or suppressed physical error rates compared to the stochastic case, and also observe hyperedges that do not appear in the corresponding Pauli-twirled models. Finally, we decode the detector error models undergoing coherent noise and find different thresholds compared to detector error models built based on the stochastic noise assumption.

We study magnetometry of gradients and homogeneous background fields along all three spatial axes using two spatially separated spin ensembles. We derive trade-off relations for the achievable estimation precision of these parameters. Dicke states, optimal for homogeneous field estimation, can be locally rotated into states sensitive to magnetic gradients by rotating the spins in one subensemble. We determine bounds for the precision for gradient metrology in the three orthogonal directions as a function of the sensitivities of the homogenous field in those directions. The resulting partially flipped Dicke state saturates the bounds above, showing similar sensitivity in two directions but significantly reduced sensitivity in the third. Exploiting entanglement between the two ensembles, this state achieves roughly twice the precision attainable by the best bipartite separable state, which is a product of local Dicke states. For small ensembles, we explicitly identify measurement operators saturating the quantum Cramér-Rao bound, while for larger ensembles, we propose simpler but suboptimal schemes. In both cases, the gradient is estimated from second moments and correlations of angular momentum operators. Our results demonstrate how the metrological properties of Dicke states can be exploited for quantum-enhanced multiparameter estimation.

Theoretical studies and experiments in the last six years have revealed the potential for novel behaviours and functionalities in device physics through the synthetic engineering of negatively-curved spaces. For instance, recent developments in hyperbolic band theory have unveiled the emergence of higher-dimensional eigenstates -- features fundamentally absent in conventional Euclidean systems. At the same time, superconducting quantum circuits have emerged as a leading platform for quantum analogue emulations and digital simulations in scalable architectures. Here, we introduce a scalable superconducting circuit framework for the analogue quantum emulation of tight-binding models on hyperbolic and kagome-like lattices. Using this approach, we experimentally realize three distinct lattices, including, for the first time to our knowledge, a hyperbolic lattice whose unit cell resides on a genus-3 Riemann surface. Our method encodes the hyperbolic metric directly into capacitive couplings between high-quality superconducting resonators, enabling tenable reproduction of spectral and localization properties while overcoming major scalability and spectral resolution limitations of previous designs. These results set the stage for large-scale experimental studies of hyperbolic materials in condensed matter physics and lay the groundwork for realizing hyperbolic quantum processors, with potential implications for both fundamental physics and quantum computing

Efficient single-photon emitters are desirable for quantum technologies including quantum networks and photonic quantum computers. We investigate the T centre, a telecommunications-band emitter in silicon, and find a strong isotope dependence of its excited-state lifetime. In particular, the lifetime of the deuterium T centre is over five times longer than the common protium variant. Through explicit first-principles calculations, we demonstrate that this dramatic difference is due to a reduction in the carbon-hydrogen local vibrational mode energy, which suppresses non-radiative decay. Our results imply that the deuterium T centre approaches unit quantum efficiency, enabling more efficient single-photon sources, quantum memories, and entanglement generation.

Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state distillation, quantum communication and cryptography, and qubit tapering. Moreover, circuits composed entirely of Clifford gates are classically simulatable, highlighting their computational significance. In this work, we extend the concept of Clifford transformations to fermionic systems. We demonstrate that fermionic Clifford transformations are generated by half-body and pair operators, providing a systematic framework for their characterization. Additionally, we establish connections with fermionic mean-field theories and applications in qubit tapering, offering insights into their broader implications in quantum computing.

Surface acoustic waves (SAWs), as Rayleigh waves generated by elastic media, have been used in gyroscopes for over 40 years due to their unique propagation characteristics. However, their working principle, based on Coriolis effects, has become increasingly ineffective for addressing modern sensing challenges in complex scenarios. Fortunately, recent advancements in quantized SAWs offer a promising solution: SAWs operating at extremely low pump powers (approximately at the single-phonon level) can exhibit substantial quantum coherence, enabling investigations into the fundamental limits of SAW gyroscopes as constrained by the Heisenberg uncertainty relation. In particular, when multiple SAWs couple to a common waveguide at distinct locations, the nonlocality arising from the spatial separation among coupling points induces directional coupling between the SAWs. To elucidate this directionality, we propose a quantum gyroscope characterized by multiplepoint couplings. Unlike traditional single-point coupling designs, our gyroscope exhibits distinctive time-delayed dynamics that depend on the system's topologies. We emphasize that these dynamics invalidate the Markovian approximation, even when the time delay is relatively small. Through a comprehensive analysis of all possible topologies, we observe that the directional coupling implies an inherent nonreciprocal transfer. This nonreciprocity confers signiffcant advantages to our gyroscope compared to traditional designs, notably enhancing both the signal-to-noise ratio and sensitivity. Speciffcally, it enables the extraction of output signals that would otherwise be obscured by noise. Consequently, our ffndings suggest that systems with multiple-point couplings and the associated nonreciprocity can serve as valuable resources for advancing quantum sensing technologies.

Photonic systems with exceptional points, where eigenvalues and corresponding eigenstates coalesce, have attracted interest due to their topological features and enhanced sensitivity to external perturbations. Non-Hermitian mode-coupling matrices provide a tractable analytic framework to model gain, loss, and chirality across optical, electronic, and mechanical platforms without the complexity of full open-system dynamics. Exceptional points define their spectral topology, and enable applications in mode control, amplification, and sensing. Yet $N$-mode couplers, the minimal setting for $N$th-order exceptional points, are often studied in specific designs that overlook their algebraic structure. We introduce a general $\mathrm{sl}(N,\mathbb{C})$ framework for arbitrary $N$-mode couplers in classical and quantum regimes, and develop it explicitly for $N=3$. This case admits algebraic diagonalization, where a propagation-dependent gauge aligns local and dynamical spectra and reveals the geometric phase connecting adiabatic and exact propagation. An exact Wei--Norman propagator captures the full dynamics and makes crossing exceptional points explicit. Our framework enables classification of coupler families. We study the family spanning $\mathcal{PT}$-symmetric and non-Hermitian cyclic couplers, where two exceptional points of order three lie within a continuum of exceptional points of order two, ruling out pure encircling. As an application, we study these exceptional points for a lossy three-leg beam splitter and reveal its propagation dynamics as a function of initial states, such as Fock and NOON states. Our approach provides a systematic route to analyze non-Hermitian mode couplers and guide design in classical and quantum platforms.

Variational quantum algorithms (VQAs) are promising tools for demonstrating quantum utility on near-term quantum hardware, with applications in optimisation, quantum simulation, and machine learning. While researchers have studied how easy VQAs are to train, the effect of quantum noise on the classical optimisation process is still not well understood. Contrary to expectations, we find that twirling, which is commonly used in standard error-mitigation strategies to symmetrise noise, actually degrades performance in the variational setting, whereas preserving biased or non-unital noise can help classical optimisers find better solutions. Analytically, we study a universal quantum regression model and demonstrate that relatively uniform Pauli channels suppress gradient magnitudes and reduce expressivity, making optimisation more difficult. Conversely, asymmetric noise such as amplitude damping or biased Pauli channels introduces directional bias that can be exploited during optimisation. Numerical experiments on a variational eigensolver for the transverse-field Ising model confirm that non-unital noise yields lower-energy states compared to twirled noise. Finally, we show that coherent errors are fully mitigated by re-parameterisation. These findings challenge conventional noise-mitigation strategies and suggest that preserving noise biases may enhance VQA performance.

Periodically driven quantum many-body systems exhibit a wide variety of exotic nonequilibrium phenomena and provide a promising pathway for quantum applications. A fundamental challenge for stabilizing and harnessing these highly entangled states of matter is system heating by energy absorption from the drive. Here, we propose and demonstrate a disorder-free mechanism, dubbed Fock space prethermalization (FSP), to suppress heating. This mechanism divides the Fock-space network into linearly many sparse sub-networks, thereby prolonging the thermalization timescale even for initial states at high energy densities. Using 72 superconducting qubits, we observe an FSP-based time-crystalline order that persists over 120 cycles for generic initial Fock states. The underlying kinetic constraint of approximately conserved domain wall (DW) numbers is identified by measuring site-resolved correlators. Further, we perform finite-size scaling analysis for DW and Fock-space dynamics by varying system sizes, which reveals size-independent regimes for FSP-thermalization crossover and links the dynamical behaviors to the eigenstructure of the Floquet unitary. Our work establishes FSP as a robust mechanism for breaking ergodicity, and paves the way for exploring novel nonequilibrium quantum matter and its applications.

High-fidelity qubit readout is a fundamental requirement for practical quantum computing systems. In this work, we investigate methods to enhance the measurement fidelity of flux qubits via a quantum flux parametron-mediated readout scheme. Through theoretical modeling and numerical simulations, we analyze the impact of different measurement bases on fidelity in single-qubit and coupled two-qubit systems. For single-qubit systems, we show that energy bases consistently outperform flux bases in achieving higher fidelity. In coupled two-qubit systems, we explore two measurement models: sequential and simultaneous measurements, both aimed at reading out a single target qubit. Our results indicate that the highest fidelity can be achieved either by performing sequential measurement in a dressed basis over a longer duration or by conducting simultaneous measurement in a bare basis over a shorter duration. Importantly, the sequential measurement model consistently yields more robust and higher fidelity readouts compared to the simultaneous approach. These findings quantify achievable fidelities and provide valuable guidance for optimizing measurement protocols in emerging quantum computing architectures.

Beams of light or matter that carry well-defined states of orbital angular momentum (OAM) are promising probes of topological and textured condensed matter systems such as magnetic skyrmions. Using spin-echo small-angle neutron scattering (SESANS), we demonstrate the production of vortex neutron beams from forked phase gratings of various topological charges. In contrast to some previous techniques used to verify OAM production, SESANS is a more precise measurement of the neutron's OAM as it is a phase-sensitive, interferometric technique that directly measures the phase between the scattered neutron spin states.

We study quantum tunneling in an asymmetric double-well potential using a dynamical systems-based approach rooted in the Ehrenfest formalism. In this framework, the time evolution of a Gaussian wave packet is governed by a hierarchy of coupled equations linking lower- and higher-order position moments. An approximate closure, required to render the system tractable, yields a reduced dynamical system for the mean and variance, with skewness entering explicitly due to the potential's asymmetry. Stability analysis of this system identifies energy thresholds for detectable tunneling across the barrier and reveals regimes where tunneling, though theoretically allowed, remains practically undetectable. Comparison with full numerical solutions of the time-dependent Schrödinger equation shows that, beyond reproducing key tunneling features, the dynamical systems approach provides an interpretable description of quantum transport through tunneling in an effective asymmetric two-level system.

Quantum entanglement serves as a fundamental resource in quantum information theory. This paper presents a comprehensive framework of separability criteria for detecting entanglement across quantum systems, from bipartite to multipartite states. We propose a novel unified parameterized extended correlation tensor, constructed via the generalized Bloch representation under an arbitrary orthogonal basis, which bridges our bipartite criterion with several existing ones. Moreover, we develop a specialized tensor unfolding technique -- termed mixed mode matrix unfolding -- that naturally generalizes the conventional $k$-mode matrix unfolding and enables the generalization of the extended correlation tensor construction to multipartite systems. And we derive several separability criteria for multipartite states. Numerical examples demonstrate that our separability criteria exhibit enhanced capability in detecting entanglement.

Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them classically tractable. Motivated by the recent success of matrix product state (MPS)-based classical simulation of Gaussian boson sampling (Oh et al., 2024), we extend this framework to investigate the classical simulability of other noisy quantum sampling models. We develop MPS-based classical algorithms for lossy boson sampling and noisy instantaneous quantum polynomial-time (IQP) sampling, both of which retain the tunable accuracy characteristic of the MPS approach through the bond dimension. Our approach constructs pure-state decompositions of noisy or lossy input states whose components remain weakly entangled after circuit evolution, thereby providing a means to systematically explore the boundary between quantum-hard and classically-simulable regimes. For boson sampling, we analyze single-photon, Fock, and cat-state inputs, showing that classical simulability emerges at transmission rates scaling as $O(1/\sqrt{N})$, reaching the known boundary of quantum advantage with a tunable and scalable method. Beyond reproducing previous thresholds, our algorithm offers significantly improved control over the accuracy-efficiency trade-off. It further extends the applicability of MPS-based simulation to broader classes of noisy quantum sampling models, including IQP circuits.

We demonstrate the possibility of a genuine quantum advantage in the efficiency of quantum batteries by analyzing a model that enables a consistent comparison between quantum and classical regimes. Our system consists of $N$ harmonic oscillator cells coupled to a common thermal reservoir, evolving through Gaussian states. We define the global efficiency as the ratio of extractable work (ergotropy) to stored energy, and derive analytical bounds that distinguish, in order of increasing efficiency, regimes characterized by classical squeezing, quantum squeezing without entanglement, and genuine entanglement. Moreover, numerical simulations support the emergence of a similar hierarchy for the thermodynamic efficiency, defined as the ratio between ergotropy and the total thermodynamic cost of the charging process.

The Unruh effect predicts that an accelerated observer perceives the Minkowski vacuum as a thermal bath, but its direct observation requires extreme accelerations beyond current experimental reach. Foundational theory [Olson & Ralph, Phys. Rev. Lett. 106, 110404 (2011)] shows that an equivalent thermal response, known as the timelike Unruh effect, can occur for detectors following specific timelike trajectories without acceleration, enabling laboratory tests with stationary yet time-dependent detectors. Here, we report a proof-of-principle demonstration of the timelike Unruh effect in a quantum system of trapped ion, where a two-level spin serves as the detector and is temporally coupled to the ambient field encoded in the ion's vibrational motion. Specifically, we study both excitation and emission dynamics of the detector moving along a spacetime trajectory in the future/past light cone, and demonstrate the thermal response of the detector to the Minkowski vacuum that resembles the Unruh effect. This work establishes a controllable tabletop platform for exploring relativistic quantum physics under accessible laboratory conditions.

The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold analyses are based on the assumption of independent and identically distributed (i.i.d.) errors. Though there are numerical studieds for threshold with correlated error, they are only the lower bond ranther than exact value, this offers potential for higher error this http URL, we establish an error-edge map, which allows for the mapping of quantum error correction to a square-octagonal random bond Ising model. We then present the exact threshold under a realistic noise model that combines independent single-qubit errors with correlated errors between nearest-neighbor data qubits. Our method is applicable for any ratio of nearest-neighbor correlated errors to i.i.d. errors. We investigate the error correction threshold of surface codes and we present analytical constraints giving exact value of error threshold. This means that our error threshold is both upper bound and achievable and hence on the one hand the existing numerical threshold values can all be improved to our threshold value, on the other hand, our threshold value is highest achievable value in principle.

Fundamental tests of quantum mechanics, such as the generation of non-classical states and tests of wavefunction collapse models, are performed on increasingly larger size and mass scales. Highly coherent mechanical resonators, which also prove invaluable in ultrasensitive microscopy methods, are essential tools towards these efforts. Studying these resonators in a thermal equilibrium state at millikelvin temperatures provides a promising path to increase their coherence time. Here, we passively cool a 700 Hz, massive (1.5 ng) mechanical cantilever down to 6.1(4)mK by means of nuclear demagnetization, as confirmed by detecting its thermal motion via a lock-in based detection scheme. At the lowest temperatures the thermal motion of the resonator is still clearly distinguishable from the background noise. Our data analysis confirms that at these temperatures the motion is still thermally distributed. These results pave the way for passiveof cooling low-frequency resonators to the sub-milllikelvin regime, which would enable new tests of quantum mechanics and advances in ultrasensitive force detection.

Quantum circuit simulators running on classical computers offer a vital platform for designing, testing, and optimizing quantum algorithms, driving innovation despite limited access to real quantum hardware. However, their scalability is inherently constrained by exponential memory and computational overhead, which restricts accurate simulation of large-scale quantum circuits and often results in approximate output distributions. Here, we propose an exact sampling algorithm that integrates tensor network contraction techniques with a Markov process, wherein a classical state evolves according to the local structure of the quantum circuit. As a demonstration, we target the challenge of generating samples from ideal and noisy QAOA circuits with up to 476 qubits, incorporating both depolarizing and amplitude damping noise models. These results enable further validation of several assumptions and conjectures at a scale previously out of reach, significantly expanding the scope of classical simulation in quantum algorithm research.

The catalytic extension of a discrete two-stroke engine employs a cyclic auxiliary system - the catalyst - that remains decoupled from the baths and performs no work, yet enhances power and efficiency beyond the corresponding non-catalytic counterpart. Theoretical models of discrete engines are relatively easy to analyze but remain challenging for experimental implementation due to the required control over individual strokes. In contrast, externally driven engines that are simultaneously coupled to both heat baths - the so-called continuous engines - are more experimentally feasible. Here, we establish an equivalence between discrete and continuous machines, both with and without a catalyst, by mapping the discrete unitary processes and thermalization steps onto an interaction Hamiltonian and a Markovian model of dissipation. As a result, by replacing probability flows with probability currents, we construct an analogous continuous machine corresponding to previously demonstrated catalytic schemes that generalize Otto engines. We illustrate this mapping for the simplest catalytic extension of the Otto engine, demonstrating catalytic enhancement in the continuous regime.

Wave guides for classical electromagnetic fields can realize the quantum evolution of the wave function for a system of qubits. Phase shifts, switches and beam splits allow for the construction of arbitrary quantum gates. They can act at once on a large number of qubits. For this correlation based photonic quantum computer the channels of the wave guides represent basis states of a multi-qubit system rather than individual qubits. The classical probabilistic implementation of a quantum evolution sheds new light on the foundations of quantum mechanics.

The energy distribution of a quantum state is essential for accurately estimating a molecule's ground state energy in quantum computing. Directly obtaining this distribution requires full Hamiltonian diagonalization, which is computationally prohibitive for large-scale systems. A more practical strategy is to approximate the distribution from a finite set of Hamiltonian moments. However, reconstructing an accurate distribution from only a limited number of moments remains a significant challenge. In this work, we introduce Jacobi-Anger Density Estimation (JADE), a non-parametric, quantum-inspired method designed to overcome this difficulty. JADE reconstructs the characteristic function from a finite set of moments using the Jacobi-Anger expansion and then estimates the underlying distribution via an inverse Fourier transform. We demonstrate that JADE can accurately recover the energy distribution of a quantum state for a molecular system. Beyond quantum chemistry, we also show that JADE is broadly applicable to the estimation of complicated probability density functions in various other scientific and engineering fields. Our results highlight JADE as a powerful and versatile tool for practical quantum systems, with the potential to significantly enhance ground state energy estimation and related applications.

Current quantum programming is dominated by low-level, circuit-centric approaches that limit the potential for compiler optimization. This work presents how a high-level programming construct provides compilers with the semantic information needed for advanced optimizations. We introduce a novel optimization that leverages a quantum-specific instruction to automatically substitute quantum gates with more efficient, approximate decompositions, a process that is transparent to the programmer and significantly reduces quantum resource requirements. Furthermore, we show how this instruction guarantees the correct uncomputation of auxiliary qubits, enabling safe, dynamic quantum memory management. We illustrate these concepts by implementing a V-chain decomposition of the multi-controlled NOT gate, showing that our high-level approach not only simplifies the code but also enables the compiler to generate a circuit with up to a 50% reduction in CNOT gates. Our results suggest that high-level abstractions are crucial for unlocking a new class of powerful compiler optimizations, paving the way for more efficient quantum computation.

There are several important philosophical problems to which quantum mechanics is often said to have made significant contributions: - Determinism: quantum theory has been taken to refute determinism; -Free Will: in turn, this is thought to open the door to free will; - The mind-body problem: relatedly, it is sometimes said to shed light on consciousness; - Idealism: more radically, quantum theory is assumed to have refuted realism and to have placed the observer at the center of the world; - Reductionism: even granting realism, it has been claimed that quantum theory undermines reductionism. Our main thesis in this paper is that none of this is either necessary or desirable. By adopting the de Broglie--Bohm theory (or Bohmian mechanics), one can straightforwardly account for quantum phenomena without endorsing any of these claims.

We derive a tight generalization bound for quantum machine learning that is applicable to a wide range of supervised tasks, data, and models. Our bound is both efficiently computable and free of big-O notation. Furthermore, we point out that previous bounds relying on big-O notation may provide misleading suggestions regarding the generalization error. Our generalization bound demonstrates that for quantum machine learning models of arbitrary size and depth, the sample size is the most dominant factor governing the generalization error. Additionally, the spectral norm of the measurement observable, the bound and Lipschitz constant of the selected risk function also influence the generalization upper bound. However, the number of quantum gates, the number of qubits, data encoding methods, and hyperparameters chosen during the learning process such as batch size, epochs, learning rate, and optimizer do not significantly impact the generalization capability of quantum machine learning. We experimentally demonstrate the tightness of our generalization bound across classification and regression tasks. Furthermore, we show that our tight generalization upper bound holds even when labels are completely randomized. We thus bring clarity to the fundamental question of generalization in quantum machine learning.

The heralded single photons' (HSPs) spectral brightness (SB) is defined as the generation rate per linewidth. As the generation rate of HSPs gets larger or the photons' linewidth becomes narrower, both of which are desirable in quantum information processing using HSPs, does the SB have a limit? We systematically studied the SB and the cross-correlation function, or equivalently, the signal-to-background ratio. The results in this study provide an answer applicable to all types of HSP sources. The answer relies on a newly defined quantity, the quality factor, which reveals how a HSP source approaches the ideal noise-free one. Furthermore, employing the HSP source based on hot atomic vapor, we achieved an SB of (7.0$\pm$0.3)$\times10^5$ pairs/s/MHz and a quality factor of 0.68$\pm$0.02 under the single-photon criterion. Both values are the highest records to date among all kinds of HSP sources.

We propose a general framework to compare the values of a physical quantity pertaining to two - or more - physical setups, in the finite-precision scenario. Such a situation requires us to compare between two "patches" on the real line instead of two numbers. Identification of extent of the patches is typically done via standard deviation, as obtained within usual quantum metrological considerations, but can not be always applied, especially for asymmetric error distributions. The extent can however be universally determined by utilizing the concept of percentiles of the probability distribution of the corresponding estimator. As an application, we introduce the concept of finite-precision cooling in a generic quantum system. We use this approach in the working of a three-qubit quantum refrigerator governed by Markovian dynamics, and demonstrate the occurrence of cooling within finite precision for both transient and steady-state regimes, across strong- and weak-coupling limits of the inter-qubit interaction.

We design and implement a quantum combinatorial reasoning framework for large language models (QCR-LLM), integrating a real quantum computer in the hybrid workflow. QCR-LLM reformulates reasoning aggregation as a higher-order unconstrained binary optimization (HUBO) problem. In this sense, reasoning fragments are represented as binary variables and their interactions encode statistical relevance, logical coherence, and semantic redundancy. We tackle the resulting high-order optimization problem both classically, via simulated annealing, and quantumly through the bias-field digitized counterdiabatic quantum optimizer (BF-DCQO) executed on IBM's superconducting digital quantum processors. Experiments on BIG-Bench Extra Hard (BBEH) benchmarks demonstrate that our QCR-LLM consistently improves reasoning accuracy across multiple LLM backbones, surpassing reasoning-native systems such as o3-high and DeepSeek R1 by up to $+9\,$pp. Despite requiring multiple reasoning samples per query, our QCR-LLM remains approximately five times more energy-efficient than o3-high, owing to the low per-token energy footprint of its GPT-4o backbone. These results constitute the first experimental evidence of quantum-assisted reasoning, showing that hybrid quantum-classical optimization can efficiently enhance reasoning coherence, interpretability, and sustainability in large-scale language models. We have opened the doors to the emergence of quantum intelligence, where harder prompts require quantum optimizers at quantum-advantage level.

Quantum networks rely on both quantum and classical channels for coordinated operation. Current architectures employ entanglement distribution and key exchange over quantum channels but often assume that classical communication is sufficiently secure. In practice, classical channels protected by traditional cryptography remain vulnerable to quantum adversaries, since large-scale quantum computers could break widely used public-key schemes and reduce the effective security of symmetric cryptography. This perspective presents a quantum-resistant network architecture that secures classical communication with post-quantum cryptographic techniques while supporting entanglement-based communication over quantum channels. Beyond cryptographic protection, the framework incorporates continuous monitoring of both quantum and classical layers, together with orchestration across heterogeneous infrastructures, to ensure end-to-end security. Collectively, these mechanisms provide a pathway toward scalable, robust, and secure quantum networks that remain dependable against both classical and quantum-era threats.

The ability to independently control higher-order statistical moments of continuous-variable quantum states would allow the direct ``shaping'' of non-Gaussian resources, with wide implications for quantum communication, computation, and metrology. Here we prove that such control is fundamentally impossible under any smooth Hamiltonian dynamics. Within the full infinite-dimensional algebra of Hamiltonian vector fields on phase space, the quadratic (symplectic) subalgebra $\mathfrak{sp}(2N,\mathbb R)$ -- and, in the single-mode case, its $\mathrm{SU}(1,1)$ representation -- is the unique hierarchy-preserving structure: only quadratic generators produce differential operators that terminate at second order and thereby decouple first and second moments from higher cumulants. Any smooth non-quadratic Hamiltonian introduces third- and higher-order derivatives in the phase-space generator, enforcing a universal coupling between the Gaussian and non-Gaussian sectors. This \emph{rigidity of the moment hierarchy} generalizes the Gaussian no-go theorems and identifies the analytic boundary between symplectic (Clifford) dynamics and the non-simulable regime beyond the Gottesman--Knill limit.

Magic state distillation plays a crucial role in fault-tolerant quantum computation and represents a major bottleneck. In contrast to traditional logical-level distillation, physical-level distillation offers significant overhead reduction by enabling direct implementation with physical gates. Magic state cultivation is a state-of-the-art physical-level distillation protocol that is compatible with the square-grid connectivity and yields high-fidelity magic states. However, it relies on the complex grafted code, which incurs substantial spacetime overhead and complicates practical implementation. In this work, we propose an efficient cultivation-based protocol compatible with the square-grid connectivity. We reduce the spatial overhead by avoiding the grafted code and further reduce the average spacetime overhead by utilizing code expansion and enabling early rejection. Numerical simulations show that, with a color code distance of 3 and a physical error probability of $10^{-3}$, our protocol achieves a logical error probability for the resulting magic state comparable to that of magic state cultivation ($\approx 3 \times 10^{-6}$), while requiring about half the spacetime overhead. Our work provides an efficient and simple distillation protocol suitable for megaquop use cases and early fault-tolerant devices.

A key challenge for quantum computers is the efficient preparation of many-body entangled states across many qubits. In this work, we demonstrate the preparation of matrix product states (MPS) using a renormalization-group(RG)-based quantum algorithm on superconducting quantum hardware. Compared to sequential generation, it has been shown that the RG-based protocol asymptotically prepares short-range correlated MPS with an exponentially shallower circuit depth (when scaling system size), but it is not yet clear for which system sizes it starts to convey an advantage. We thus apply this algorithm to prepare a class of MPS exhibiting a phase transition between a symmetry-protected topological (SPT) and a trivial phase for systems of up to 80 qubits. We find that the reduced depth of the RG-based circuits makes them more resilient to noise, and that they generally outperform the sequential circuits for large systems, as we showcase by measuring string-order-like local expectation values and energy densities. We thus demonstrate that the RG-based protocol enables large-scale preparation of MPS and, in particular, SPT-ordered states beyond the fixed point.

The construction of parent Hamiltonians that possess a given state as their ground state is a well-studied problem. In this work, we generalize this notion by considering simple quantum states and examining the local Hamiltonians that have these states as exact this http URL states often correspond to Quantum Many-Body Scars (QMBS) of their respective parent this http URL by earlier works on Hamiltonians with QMBS, in this work we formalize the differences between three distinct types of parent Hamiltonians, which differ in their decompositions into strictly local terms with the same eigenstates. We illustrate this classification using the $W$ state as the primary example, for which we rigorously derive the complete set of local parent Hamiltonians, which also allows us to establish general results such as the existence of asymptotic QMBS, and distinct dynamical signatures associated with the different parent Hamiltonian types. Finally, we derive more general results on the parent Hamiltonian types that allow us to obtain some immediate results for simple quantum states such as product states, where only a single type exists, and for short-range-entangled states, for which we identify constraints on the admissible types. Altogether, our work opens the door to classifying the rich structures and dynamical properties of parent Hamiltonians that arise from the interplay between locality and QMBS.

Spatial chaos as a phenomenon of ultimate complexity requires the efficient numerical algorithms. For this purpose iterative low-dimensional maps have demonstrated high efficiency. Natural generalization of Feigenbaum and Ikeda maps may include convolution integrals with kernel in a form of Green function of a relevant linear physical system. It is shown that such iterative $nonlocal$ $nonlinear$ $maps$ are equivalent to ubiquitous class of nonlinear partial differential equations of Ginzburg-Landau type. With a Green functions relevant to generic optical resonators these $nonlocal$ $maps$ emulate the basic spatiotemporal phenomena as spatial solitons, vortex eigenmodes breathing via relaxation oscillations mediated by noise, vortex-vortex and vortex-antivortex lattices with periodic location of vortex cores. The smooth multimode noise addition facilitates the selection of stable entities and elimination of numerical artifacts.

A paradigmatic model, the $\mathbb{Z}_2$ lattice gauge theory exhibits confinement mediated by the gauge field that binds pairs of particles into mesons, drawing connections to quantum chromodynamics. In the absence of any additional attractive interactions between particles, mesons are not known to bind in this model. Here, we show that resonant pair-production terms give rise to an additional repulsive binding mechanism that forms a stable ``hadron'' bound state of two mesons. A high-energy state, the hadron is stabilized by being off-resonantly coupled to a continuum. We study the dynamical formation of this bound state starting from local excitations. We use matrix product state techniques based on the time-evolving block decimation algorithm to perform our numerical simulations and analyze the effect of model parameters on hadron formation. Furthermore, we derive an effective model that explains its formation. Our findings are amenable to experimental observation on modern quantum hardware from superconducting qubits to trapped ions.

An internal symmetry in a lattice model is said to be onsiteable if it can be disentangled into an onsite action by introducing ancillas and conjugating with a finite-depth circuit. A standard lore holds that onsiteability is equivalent to being anomaly-free, which is indeed valid for finite 0-form symmetries in (1+1)D. However, for higher-form symmetries, these notions become inequivalent: a symmetry may be onsite while still anomalous. In this work, we clarify the conditions for onsiteability of higher-form symmetries by proposing an equivalence between onsiteability and the possibility of $higher$ gauging. For a finite 1-form symmetry in (2+1)D, we show that the symmetry is onsiteable if and only if its 't Hooft anomaly satisfies a specific algebraic condition that ensures the symmetry can be 1-gauged. We further demonstrate that onsiteable 1-form symmetry in (2+1)D can always be brought into transversal Pauli operators by ancillas and circuit conjugation. In generic dimensions, we derive necessary conditions for onsiteability using lattice 't Hooft anomaly of higher-form symmetry, and conjecture a general equivalence between onsiteability and possibility of higher gauging on lattices.

At a generic volume- to area-law entanglement transition in a many-body system, quantum chaos is arrested. We argue that this tends to imply the vanishing of a certain "mass" term in the field theory of the measurement-induced phase transition (MIPT) for monitored, interacting fermions. To explore this idea, we consider the MIPT with no conserved quantities that describes 1D monitored, interacting Majorana fermions in class DIII. We conjecture that the MIPT is the noninteracting DIII one in this case; the volume-law phase arises through the dangerously irrelevant mass. We propose numerical tests of our conjecture and analytically identify a candidate noninteracting critical point.

We study one dimensional quantum spin chains whose nearest neighbor interactions are random matrices that square to one. By employing free probability theory, we establish a mapping from the many-body quantum dynamics of energy density in the original chain to a single-particle hopping dynamics when the local Hilbert space dimension is large. The hopping occurs on the Cayley graph of an infinite Coxeter reflection group. Adjacency matrices on large finite clusters of this Cayley graph can be constructed numerically by leveraging the automatic structure of the group. The density of states and two-point functions of the local energy density are approximately computed and consistent with the physics of a generic local Hamiltonian: Gaussian density of states and thermalization of energy density. We then ask what happens to the physics if we modify the group on which the hopping dynamics occurs, and conjecture that adding braid relations into the group leads to integrability. Our results put into contact ideas in free probability theory, quantum mechanics of hyperbolic lattices, and the physics of both generic and integrable Hamiltonian dynamics.

We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal properties regarding corner entanglement. These universal properties follow from a set of locally-checkable conditions on the wavefunction. We also define a quantity $(\mathfrak{c}_{\text{tot}})_{\text{min}}$ that reflects the robustness of corner entanglement contributions, and show that it provides an obstruction to a gapped boundary. One reward from our analysis is that we can construct a local gapped Hamiltonian within the same chiral gapped phase from a given wavefunction; we conjecture that it is closer to the low-energy renormalization group fixed point than the original parent Hamiltonian. Our analysis of corner entanglement reveals the emergence of a universal conformal geometry encoded in the entanglement structure of bulk regions of chiral gapped states that is not visible in topological field theory.

We investigate quantum-information-theoretic observables in electron-proton scattering at the Electron-Ion Collider (EIC). Our analysis focuses on entanglement and magic, two complementary indicators of non-classicality in quantum states. We show that while unpolarized and longitudinally polarized beams yield unentangled separable outcomes, transverse beam polarization enables the generation of entangled and non-stabilizer states. This result holds for both elastic and deep inelastic electron-proton scattering in QED. In the deep inelastic regime, the degree of quantum correlation is governed by the transversity parton distribution functions, providing a novel perspective on spin dynamics within QCD. These results establish the EIC as a promising environment for generating entangled and non-stabilizer states in high-energy physics, and they highlight opportunities for future lepton-hadron colliders to extend such studies into new kinematic domains.

We study superselection sectors in two-dimensional quantum spin systems with an on-site action of a compact abelian group $G$. Naaijkens and Ogata (2022) arXiv:2102.07707 showed that for states quasi-equivalent to a product state, the superselection structure is trivial, reflecting the absence of long-range entanglement. We consider a symmetry-compatible refinement of this setting, in which both the superselection criterion and the notion of equivalence between representations are required to respect the $G$-action. Under this stricter notion of equivalence, the sector structure for a $G$-equivariant product representation becomes nontrivial: the $G$-equivariant superselection sectors are classified by elements of the Pontryagin dual $\widehat{G}$. This shows that even in phases without long-range entanglement, imposing symmetry compatibility can lead to nontrivial sector structure.

We demonstrate the non-spreading behavior of Airy wave packets utilizing the Feynman path integral formulation of a linear potential, the Airy functions' zeros correspondence to heavy-meson mass spectroscopy, and their implications to the eigenstates of ultra-cold neutrons in Earth's gravitational field. We derive the linear kernel, and utilize the Feynman path integral time evolution to show that Airy function wave packets are non-dispersive in free space. We then model the confining contribution to 1S - 2S heavy meson mass gaps as a 1+1D absolute linear potential and look at the correspondence of the Airy function zeros. In doing so, we predicted the confining contribution to the mass gap of heavy mesons with a good accuracy when compared to calculations performed in the light front. Furthermore, we used these Airy function solutions to model the quantum states of a neutron under Earth's gravity. We show that the measured heights of a neutron can be modeled by the zeros of the Airy function, and compare to experimental data and predictions utilizing the WKB approximation.

We investigate the quantum statistical properties of the confining string connecting a static fermion-antifermion pair in the massive Schwinger model. By analyzing the reduced density matrix of the subsystem located in between the fermion and antifermion, we demonstrate that as the interfermion separation approaches the string-breaking distance, the overlap between the microscopic density matrix and an effective thermal density matrix exhibits a pronounced, narrow peak, approaching unity at the onset of string breaking. This behavior reveals that the confining flux tube evolves toward a genuinely thermal state as the separation between the charges grows, even in the absence of an external heat bath. In other words, one cannot tell whether a reduced state of the subsystem arises from a surrounding heat bath or from entanglement with the rest of the system. The entanglement spectrum near the critical string-breaking distance exhibits a rapid transition from the dominance of a single state describing the confining electric string towards a strongly entangled state containing virtual fermion-antifermion pairs. Our findings establish a quantitative link between confinement, entanglement, and emergent thermality, and suggest that string breaking corresponds to a microscopic thermalization transition within the flux tube.

We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework to derive the Principal Principle -- the norm that rational credence should match known objective chance -- without circularity. The derivation brings together de Finetti's exchangeability, Martin-Löf randomness, Lewis's and Skyrms's chance-credence norms, and statistical constraining laws (arXiv:2303.01411). Laws that constrain histories to algorithmically random sequences naturally pair with exchangeable credences encoding inductive symmetries. Using the de Finetti representation theorem, we show that this pairing directly entails the Principal Principle of this framework. We extend the proof to partial exchangeability and provide finite-history bounds that vanish in the infinite limit. The Principal Principle thus emerges as a mathematical consequence of the alignment between nomological constraints and inductive learning. This reveals how algorithmic randomness and exchangeability can illuminate foundational questions about chance, frequency, and rational belief.

We present a unified, SI-consistent framework to constrain minimal SME coefficients $a_\mu$ and $b_\mu$ using magnetically confined two-dimensional electron systems under a uniform magnetic field. Working in the nonrelativistic (Schrödinger--Pauli) limit with effective mass, we derive the radial problem for cylindrical geometries and identify how spatial components ($\mathbf a,\mathbf b$) reshape the effective potential, via $1/r$ and $r$ terms or spin-selective offsets, while scalar components ($a_0,b_0$) act through a global energy shift and a spin-momentum coupling. Phenomenological upper bounds follow from requiring LV-induced shifts to lie below typical spectroscopic resolutions: $|a_0|\lesssim\delta E$, $|b_z|\lesssim\delta E/\hbar$, and compact expressions for $|a_\varphi|$ and $|b_0|$ that expose their dependence on device scales ($r_0$, $B_0$, $\mu$, $m$). Dimensional analysis clarifies that, in this regime, spatial $a_i$ carry momentum dimension and $b_i$ carry inverse-time/length dimensions, ensuring gauge-independent, unit-consistent reporting. Finite-difference eigenvalue calculations validate the scaling laws and illustrate spectral signatures across realistic parameter sets. The results show that scalar sectors (notably $a_0$) are tightly constrained by state-of-the-art $\mu$eV-resolution probes, while spatial and axial sectors benefit from spin- and $m$-resolved spectroscopy and geometric leverage, providing a reproducible pathway to test Lorentz symmetry in condensed-matter platforms.

Entanglement is a fundamental resource in quantum information science, with profound implications for computing, communication, and metrology. Nuclear scattering processes, dominated by rich spin-dependent interactions, offer a natural platform for generating complex spin entanglement. Here, using proton-proton scattering as a quantum laboratory, we report the emergence of a near-pure Bell-triplet state at a laboratory energy of 151 MeV and a center-of-mass scattering angle of 90 degrees, with the spin amplitude a transition operator connecting two different Bell states. In contrast to the low-energy singlet state governed by the Pauli principle and the S-wave dominance, this second maximally entangled state is directly shaped by tensor forces beyond leading-order chiral effective field theory, providing a distinct quantum-information signature for realistic nuclear forces. These findings, invisible to traditional scattering observables, establish proton-proton scattering as a robust source of triplet entanglement and pave the way for next-generation nuclear Bell tests.

Supersolidity in a dipolar Bose-Einstein condensate (BEC), which is the coexistence of crystalline density modulation and global phase coherence, emerges from the interplay of contact interactions, long-range dipole-dipole forces, and quantum fluctuations. Although realized experimentally, stabilizing this phase at zero temperature often requires high peak densities. Here we chart the finite-temperature phase behavior of a harmonically trapped dipolar BEC using an extended mean-field framework that incorporates both quantum (Lee-Huang-Yang) and thermal fluctuation effects. We find that finite temperature can act constructively: it shifts the supersolid phase boundary toward larger scattering lengths, lowers the density threshold for the onset of supersolidity, and broadens the stability window of modulated phases. Real-time simulations reveal temperature-driven pathways (crystallization upon heating and melting upon cooling) demonstrating the dynamical accessibility and path dependence of supersolid order. Moreover, moderate thermal fluctuations stabilize single-droplet states that are unstable at zero temperature, expanding the experimentally accessible parameter space. These results identify temperature as a key control parameter for engineering and stabilizing supersolid phases, offering realistic routes for their observation and control in dipolar quantum gases.

We theoretically predict the interaction between polaritonic excitations arising from the coupling of a cavity photon mode with bound to continuum intersubband transitions in a doped quantum well. The resulting exciton bound by photon exchange, recently demonstrated experimentally, exhibits a binding energy that can be continuously tuned by varying the cavity frequency. We show that polariton-polariton interactions, originating from both Coulomb interactions and Pauli blocking, can be dramatically enhanced by reducing the exciton binding energy, thereby increasing the effective Bohr radius along the growth direction. This regime is reminiscent of Rydberg atoms, where weak binding leads to strong quantum interactions. Our predictions indicate that this physics can give rise to giant quantum optical nonlinearities in the mid and far infrared, a spectral region that remains largely unexplored in quantum optics and offers exciting opportunities for both fundamental studies and applications.

We prove that the semiclassical Einstein equations emerge directly from quantum information theory. Using modular theory, we establish that the relative entropy between the vacuum state and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across the horizon. Under the assumption of the Bekenstein-Hawking entropy-area formula, this energy flux is proportional to a variation in the surface area of the horizon cross section. The semiclassical Einstein equations follow automatically from this identification. Our approach provides a rigorous quantum field theoretic generalization of Jacobson's thermodynamic derivation of Einstein's equations, replacing classical thermodynamic entropy with the well-defined quantum relative (Araki-Uhlmann) entropy. This suggests that quantum information plays a fundamental role in what is seen as a zeroth order approximation of a theory of quantum gravity, namely quantum field theory in curved spacetimes.

Accurately observing the rarefied media of the upper atmosphere, exosphere, and planetary and solar system environments and beyond requires highly sensitive metrological techniques. We present the operating concept and architecture of an in-situ sensing solution based on the dynamics of a levitated nanoparticle (levitodynamics). It can detect and measure impacts of individual particles in rarefied media. Dubbed `LEVITAS', our sensor consists of a dispenser of dielectric nanoparticles and optical trapping of a single nanoparticle in the focus of a laser beam. The trapped nanoparticle constitutes a harmonic oscillator at frequencies in the kilohertz range whose position can be tracked at the standard quantum limit by interferometric detection of the laser photons it scatters. Here, we simulate microcanonical impacts on the nanoparticle and show that the density, velocity, temperature, and composition of the surrounding medium can be estimated accurately. We illustrate the performance of LEVITAS in circumstances ranging from low Earth orbit out to exospheric distances, across which individual impacts can be detected at favourable rates. Furthermore, LEVITAS may be employed to accurately measure highly rarefied neutral distributions within vastly different areas of momentum space. This we demonstrate by simulating the measurement of high-velocity neutral gas particles from the interstellar medium penetrating the heliosphere and flowing through our solar system.

We develop a preconditioned nonlinear conjugate-gradient solver for ground states of binary dipolar Bose-Einstein condensates within the extended Gross-Pitaevskii equation including Lee-Huang-Yang corrections. The optimization is carried out on the product-of-spheres normalization manifold and combines a manifold-preserving analytic line search, derived from a second-order energy expansion and validated along the exact normalized path, with complementary Fourier-space kinetic and real-space diagonal (Hessian-inspired) preconditioners. The method enforces monotonic energy descent and exhibits robust convergence across droplet, stripe, and supersolid regimes while retaining spectrally accurate discretizations and FFT-based evaluation of the dipolar term. In head-to-head benchmarks against imaginary-time evolution on matched grids and tolerances, the solver reduces iteration counts by one to two orders of magnitude and overall time-to-solution, and it typically attains slightly lower energies, indicating improved resilience to metastability. We reproduce representative textures and droplet-stability windows reported for dipolar mixtures. These results establish a reliable and efficient tool for large-scale parameter scans and phase-boundary mapping, and for quantitatively linking numerically obtained metastable branches to experimentally accessible states.

For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic limit, examining them is beneficial for a sharper understanding of how the limit is attained. We contrast a classical and a quantum model of particle-wall correlations within the canonical ensemble.

For any element $g$ of compact reductive group $G$ we investigate the asymptotic behavior of its normalized irreducible character in the high-dimension limit, $\frac{\chi_\lambda(g)}{d_\lambda}$. We show that when $G$ is simple the limit vanishes besides identity element. For semisimple groups one gets the same results under the additional assumption that dimensions of irreducible representations of all simple components are going to infinity. Using the notion of approximate $t$-designs we connect this observations with bounds on the production of quantum randomness in large quantum systems.

We introduce the notion of a field of covariances, a contravariant functor from non-commutative probability spaces to Hilbert spaces, as the natural categorical analogue of statistical covariance. In the case of finite-dimensional non-commutative probability spaces, we obtain a complete classification of such fields. Our results unify classical and quantum information geometry: in the tracial case, we recover (a contravariant version of) Cencov's uniqueness of the Fisher-Rao metric, while in the faithful case, we recover (a contravariant version of) the Morozova-Cencov-Petz classification of quantum monotone metrics. Crucially, our classification extends naturally to non-faithful states that are not pure, thus generalizing Petz and Sudar's radial extension.

Quantum Mpemba effect occurs when a quantum system, residing far away from the steady state, relaxes faster than a relatively nearer state. We look for the presence of this highly counterintuitive effect in the relaxation dynamics of the operators within the open quantum system setting. Since the operators evolve under a non-trace preserving map, the trace distance of an operator is not a monotonically decaying function of time, unlike its quantum state counterpart. Consequently, the trace distance can not serve as a reliable measure for detecting the Mpemba effect in operator dynamics. We circumvent this problem by defining a \textit{dressed} distance between operators that decays monotonically with time, enabling a generalized framework to explore the Mpemba-like effect for operators. Applying the formalism to various open quantum system settings, we find that, interestingly, in the single qubit case, only accelerated relaxation of operators is possible, while genuine Mpemba-like effects emerge in higher-dimensional systems such as qutrits and beyond. Furthermore, we demonstrate the existence of Mpemba-like effects in nonlocal, non-equilibrium operators, such as current, in a double-quantum-dot setup. Our results, besides offering fundamental insight about the occurrence of the Mpemba-like effect under non-trace preserving dynamics, open avenues for new experimental studies where quicker relaxation of observables could be of significant interest.

Using an ultracold gas of $^{87}$Rb$^{133}$Cs molecules, we perform hyperfine-resolved spectroscopy of transitions from the vibronic ground state to the lowest rovibrational states of the electronic state $\mathrm{b}^3\Pi_0$, as a function of magnetic field. These transitions are spin forbidden, resulting in narrow linewidths, and feature near-diagonal Franck-Condon factors. We develop a model of the hyperfine and Zeeman structure that includes coupling between the $0^+$ and $0^-$ components of $\mathrm{b}^3\Pi_0$. We fit the spectra to obtain rotational and hyperfine coupling constants. We measure transition dipole moments associated with specific transitions by directly observing Rabi oscillations as a function of a resonant laser pulse duration. Using resonant $\pi$ pulses, we prepare molecules in the electronically excited state and directly measure the spontaneous emission rate.

We investigate long-range resonances in quasiperiodic many-body localized (MBL) systems. Focusing on the Heisenberg chain in a deterministic Aubry-André potential, we complement standard diagnostics by analyzing the structure of long-distance pairwise correlations at high energy. Contrary to the expectation that the ergodic-MBL transition in quasiperiodic systems should be sharper due to the absence of Griffiths regions, we uncover a broad unconventional regime at strong quasiperiodic potential, characterized by fat-tailed distributions of longitudinal correlations at long distance. This reveals the presence of atypical eigenstates with strong long-range correlations in a regime where standard diagnostics indicate stable MBL. We further identify these anomalous eigenstates as quasi-degenerate pairs of resonant cat states, which exhibit entanglement at long distance. These findings advance the understanding of quasiperiodic MBL and identify density-correlation measurements in ultracold atomic systems as a probe of long-range resonances.

Shortcuts to adiabaticity (STA) have been successfully applied both theoretically and experimentally to a wide variety of quantum control tasks. In previous work the authors have developed an analytic extension to shortcuts to adiabaticity, called enhanced shortcuts to adiabaticity (eSTA), that extends STA methods to systems where STA cannot be applied directly [Phys. Rev. Research 2, 023360 (2020)]. Here we generalize this approach and construct an alternative eSTA method that takes advantage of higher order terms. We apply this eSTA method to the expansion of both a Gaussian trap and accordion lattice potential, demonstrating the improved fidelity and robustness of eSTA.

The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first step in formalising the hypothesis that quantum measurements are driven by the natural tendency of closed systems to maximize entropy, a notion that we call the Measurement-Equilibration Hypothesis. In this paradigm, we investigate how classical measurement outcomes can emerge within a purely unitary framework, and find that: (i) the interactions used in standard measurement models fail to spontaneously encode information classically and (ii) while ideal projective measurements are impossible, one can (for a given form of Hamiltonian) approximate them exponentially well as more physical systems are collected together into an ``observer'' system. We thus lay the groundwork for self-contained models of quantum measurement, proposing improvements to our simple scheme.

In recent years, achieving verifiable quantum advantage on a NISQ device has emerged as an important open problem in quantum information. The sampling-based quantum advantages are not known to have efficient verification methods. This paper investigates the verification of quantum advantage from a cryptographic perspective. We establish a strong connection between the verifiability of quantum advantage and cryptographic and complexity primitives, including efficiently samplable, statistically far but computationally indistinguishable pairs of (mixed) quantum states ($\mathsf{EFI}$), pseudorandom states ($\mathsf{PRS}$), and variants of minimum circuit size problems ($\mathsf{MCSP}$). Specifically, we prove that a) a sampling-based quantum advantage is either verifiable or can be used to build $\mathsf{EFI}$ and even $\mathsf{PRS}$ and b) polynomial-time algorithms for a variant of $\mathsf{MCSP}$ would imply efficient verification of quantum advantages. Our work shows that the quest for verifiable quantum advantages may lead to applications of quantum cryptography, and the construction of quantum primitives can provide new insights into the verifiability of quantum advantages.

Cavity optomechanics, providing an inherently nonlinear interaction between photons and phonons, have shown enomerous potential in generating macroscopic quantum entanglement. Here we propose to realize diverse bipartite and tripartite entanglement in cavity-magnon optomechanics. By introducing magnons to standard cavity optomechanics, not only tunable optomechanical entanglement and magnon-magnon entanglement can be achieved, but also flexible tripartite entanglement including magnon-photon-phonon entanglement, magnon-magnon-photon and -phonon entanglement can be generated. Moreover, optimal bipartite and tripartite entanglement can be achieved by tuning parameters. We further show that all entanglement can be enhanced via engineering the magnon-photon coupling, and is proven to be robust against the bath temperature within the survival temperature. Besides, we find that the optomechanical entanglement can be protected or restored by bad magnons with large decay rate, while other entanglement is severely reduced. The results indicate that our proposal provides a novel avenue to explore and control tunable macroscopic quantum effects in hybrid cavity-magnon optomechanics.

In this paper, we introduce the gauge-fixed QLDPC surgery scheme, an improved logical measurement scheme based on the construction of Cohen et al. (Sci. Adv. 8, eabn1717). Our scheme leverages expansion properties of the Tanner graph to substantially reduce the space overhead of QLDPC surgery. In certain cases, we only require $\Theta(w)$ ancilla qubits to fault-tolerantly measure a weight $w$ logical operator. We provide rigorous analysis for the code distance and fault distance of our schemes, and present a modular decoding algorithm that achieves maximal fault-distance. We further introduce a bridge system to facilitate fault-tolerant joint measurements of logical operators. Augmented by this bridge construction, our scheme can be used to connect different families of QLDPC codes into one universal architecture. Applying our toolbox, we show how to perform all logical Clifford gates on the [[144,12,12]] bivariate bicycle code. Our scheme adds 103 ancilla qubits into the connectivity graph, and one of the twelve logical qubits is used as an ancilla for gate synthesis. Logical measurements are combined with the automorphism gates studied by Bravyi et al. (Nature 627, 778-782) to implement 288 Pauli product measurements. We demonstrate the practicality of our scheme through circuit-level noise simulations, leveraging our proposed modular decoder that combines BPOSD with matching.

The Quantum Approximate Optimisation Algorithm (QAOA) is a widely studied quantum-classical iterative heuristic for combinatorial optimisation. While QAOA targets problems in complexity class NP, the classical optimisation procedure required in every iteration is itself known to be \NP-hard. Still, advantage over classical approaches is suspected for certain scenarios, but nature and origin of its computational power are not yet satisfactorily understood. By introducing means of efficiently and accurately approximating the QAOA optimisation landscape from solution space structures, we derive a new algorithmic variant of unit-depth QAOA for two-level Hamiltonians (including all problems in NP): Instead of performing an iterative quantum-classical computation for each input instance, our non-iterative method is based on a quantum circuit that is instance-independent, but problem-specific. It matches or outperforms unit-depth QAOA for key combinatorial problems, despite reduced computational effort. Our approach is based on proving a long-standing conjecture regarding instance-independent structures in QAOA. By ensuring generality, we link existing empirical observations on QAOA parameter clustering to established approaches in theoretical computer science, and provide a sound foundation for understanding the link between structural properties of solution spaces and quantum optimisation.

Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the dynamics of open quantum systems governed by Lindbladians. We introduce a new approximation channel for short-time evolution, inspired by the quantum trajectory method, which underpins the efficiency of our algorithms. The first algorithm achieves a gate complexity independent of the number of jump operators, $m$, marking a significant improvement in efficiency. The second algorithm achieves near-optimal dependence on the evolution time $t$ and precision $\epsilon$ and introduces only an additional $\tilde{O}(m)$ factor, which strictly improves upon state-of-the-art gate-based quantum algorithm that has an $\tilde O(m^2)$ factor. The improvement stems from the integration of the new approximation channel with a novel structured linear combination of unitaries method. In both our algorithms, the reduction of dependence on $m$ significantly enhances the efficiency of simulating practical dissipative processes characterized by a large number of jump operators.

This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By employing generalized canonical transformations, we reformulated the path integral to develop an explicit expression for the propagator. This formalism is applied to specific cases, including a Dunkl-harmonic oscillator with time-dependent mass and frequency. Solutions for the Dunkl-Caldirola-Kanai oscillator and a model with a strongly pulsating mass are derived, providing exact propagator expressions and corresponding wave functions. These findings extend the utility of Dunkl operators in quantum mechanics, offering new insights into the dynamics of time-dependent quantum systems.

Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry$^{\dagger}$ (TRS$^{\dagger}$), coinciding with those of non-Hermitian random matrices in the same symmetry class. Here, we analytically study the spectral correlations of non-Hermitian random matrices in the presence of TRS$^{\dagger}$ with signs $+1$ and $-1$, corresponding to symmetry classes AI$^{\dagger}$ and AII$^{\dagger}$, respectively. Using the fermionic replica non-linear sigma model approach, we derive $n$-fold integral expressions for the $n$th moment of the one-point and two-point characteristic polynomials. Performing the replica limit $n\to 0$, we qualitatively reproduce the density of states and level-level correlations of non-Hermitian random matrices with TRS$^{\dagger}$.

Out-of-equilibrium phases in many-body systems constitute a new paradigm in quantum matter - they exhibit dynamical properties that may otherwise be forbidden by equilibrium thermodynamics. Among these non-equilibrium phases are periodically driven (Floquet) systems [1-5], which are generically difficult to simulate classically because of their high entanglement. Here we realize a Floquet topologically ordered state theoretically proposed in ref. [6], on an array of superconducting qubits. We image the characteristic dynamics of its chiral edge modes and characterize its emergent anyonic excitations. Devising an interferometric algorithm allows us to introduce and measure a bulk topological invariant to probe the dynamical transmutation of anyons for system sizes up to 58 qubits. Our work demonstrates that quantum processors can provide key insights into the thus-far largely unexplored landscape of highly entangled non-equilibrium phases of matter.

Zero-noise extrapolation (ZNE) is a widely used quantum error mitigation technique that artificially amplifies circuit noise and then extrapolates the results to the noise-free circuit. A common ZNE approach is Richardson extrapolation, which relies on polynomial interpolation. Despite its simplicity, efficient implementations of Richardson extrapolation face several challenges, including approximation errors from the non-polynomial behavior of noise channels, overfitting due to polynomial interpolation, and exponentially amplified measurement noise. This paper provides a comprehensive analysis of these challenges, presenting bias and variance bounds that quantify approximation errors. Additionally, for any precision $\varepsilon$, our results offer an estimate of the necessary sample complexity. We further extend the analysis to polynomial least squares-based extrapolation, which mitigates measurement noise and avoids overfitting. Finally, we propose a strategy for simultaneously mitigating circuit and algorithmic errors in the Trotter-Suzuki algorithm by jointly scaling the time step size and the noise level. This strategy provides a practical tool to enhance the reliability of near-term quantum computations. We support our theoretical findings with numerical experiments.

Motivated both by classical physics problems associated with ``Newton's bucket'' and recent developments related to QCD in rotating frames of reference relevant to heavy ion collisions, we discuss the difference between ``active'' and ``passive'' rotations in quantum systems. We examine some relevant potentials and give general symmetry arguments to give criteria where such rotations give the same results. We close with a discussion of how this can be translated to quantum field theory.

Demonstrating how long-range entangled states are born from product states has gained much attention, which is not only important for quantum technology but also provides an unconventional tool in characterizing and classifying exotic phases of matter. In this paper, we introduce a unified and efficient framework of quantum circuits (i.e., a series of local unitary transformations), termed the \emph{Seed-Entangler-Enriched Sequential Quantum Circuit} (SEESQC) to construct long-range entangled states (i.e., code states) in code space of topological error-correcting codes. Specifically, we apply SEESQC to construct code states of Tetra-Digit models -- a broad class of long-range entangled stabilizer codes indexed by a four-digit parameter. These models are not rare but encompass Toric Codes across arbitrary dimensions and subsume the X-cube fracton code as special cases. Featuring a hierarchical structure of generalized entanglement renormalization group, many Tetra-Digit models host spatially extended excitations (e.g., loops, membranes, and exotic non-manifold objects) with constrained mobility and deformability, and exhibit system-size-dependent ground state degeneracies that scale exponentially with a polynomial in linear sizes. In this work, we begin with graphical and algebraic demonstration of quantum circuits for computational basis states, before generalizing to broader cases. Central to this framework is a key ingredient termed the \emph{seed-entangler} acting on a small number of qubits termed \textit{seeds}, enabling a systematic scheme to achieve arbitrary code states. Remarkably, the number of available seeds equals the number of logical qubits for the constructed examples, which leaves plenty of room for future investigation in theoretical physics, mathematics and quantum information science. Beyond the critical limitation of prior state-engineering methodologies, ...

In both classical and quantum physics, irreversible processes are described by maps that contract the space of states. The change in volume has often been taken as a natural quantifier of the amount of irreversibility. In Bayesian inference, loss of information results in the retrodiction for the initial state becoming increasingly influenced by the choice of reference prior. In this paper, we import this latter perspective into physics, by quantifying the irreversibility of any process with its Bayesian subjectivity -- that is, the sensitivity of its retrodiction to one's prior. From this perspective, we review analytical and numerical results that highlight both intuitive and subtle insights that this measure sheds on irreversible processes.

We theoretically investigate the collective dipole-dipole interactions in atoms coupled to a nanophotonic microring resonator. The atoms can interact with each other through light-induced dipole-dipole interactions mediated by free space and through the resonator whispering-gallery modes. The differing characteristics and mismatched wavenumbers of these modes give rise to complex dynamics and provide new opportunities for controlling light-matter interactions. We explore these phenomena in the context of an experimentally realized atom cloud and study the potential of the proposed sub-wavelength atom arrays.

Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step decreases exponentially with the circuit depth. This theoretical finding is validated by our numerical results over various Hamiltonians, initial states, and noise channels. Furthermore, we derive the optimal number of Trotter steps and the noise requirement to guarantee total simulation precision. To explicitly show the requirements for robust quantum simulation, we plot a phase diagram of the accumulated error in terms of circuit depth and noise rate. At last, we demonstrate that our improved error analysis leads to significant resourcesaving for fault-tolerant Trotter circuits. By addressing these aspects, this work provides fresh and systematic insight on the practical quantum advantage through quantum simulation.

Photoisomerization, a photochemical process underlying many biological mechanisms, has been modeled recently within the quantum resource theory of thermodynamics. This approach has emerged as a promising tool for studying fundamental limitations to nanoscale processes independently of the microscopic details governing their dynamics. On the other hand, correlations between physical systems have been shown to play a crucial role in quantum thermodynamics by lowering the work cost of certain operations. Here, we explore quantitatively how correlations between multiple photoswitches can enhance the efficiency of photoisomerization beyond that attainable for single molecules. Furthermore, our analysis provides insights into the interplay between quantum and classical correlations in these transformations.

We introduce an extension of the time-dependent variational Monte Carlo (tVMC) method that adaptively controls the expressivity of the variational quantum state during the simulation of the dynamics. This adaptive tVMC (atVMC) approach is specifically designed to enhance numerical stability when overparameterized variational ansätze lead to ill-conditioned equations of motion. Building on the concept of the local-in-time error (LITE), a measure of the deviation between variational and exact evolution, we introduce a procedure to quantify each parameter's contribution to reducing the LITE, using only quantities already computed in standard tVMC simulations. These relevance estimates guide the selective evolution of only the most significant parameters at each time step, while maintaining a prescribed level of accuracy. We benchmark the algorithm on quantum quenches in the one-dimensional transverse-field Ising model using both spin-Jastrow and restricted Boltzmann machine wave functions, with an emphasis on overparameterized regimes. The adaptive scheme significantly improves numerical stability and reduces the need for strong regularization, enabling reliable simulations with highly expressive variational ansätze.

In this paper, we describe some interesting properties of a spin-boson system with non-Hermitian coupling. For this particular model, it is known that the Hilbert space can be described by infinitely-many two-dimensional invariant (closed) subspaces, together with the global ground state. We expose the appearance of exceptional points on such two-dimensional subspaces, together with quantum phase transitions marking the transition from real to complex eigenvalues. We also compute the spin-boson entanglement entropy on each invariant subspace to show that the two phases can be distinguished by their distinct entanglement-entropy profiles.

Quantum sensors based on spin-defect relaxation have become powerful tools for detecting faint magnetic signals, yet their operation has remained largely confined to low magnetic fields and gigahertz frequencies. Extending such sensors into high-field ($> 0.3$ T) and sub-terahertz regimes would enable quantum metrology across a wide range of electromagnetic phenomena and scientific applications, but has proven challenging. Here, we demonstrate that negatively charged boron vacancies ($\mathrm{V_B^-}$) in two-dimensional hexagonal boron nitride can function as relaxation-based quantum sensors operating up to 0.2 terahertz. Their uniform spin-orientation and persistent spin-contrast at high fields enable direct measurement of intrinsic spin relaxation across previously unexplored temperature and frequency regimes. We also reveal a crossover in relaxation behavior \textemdash initially decreasing at low fields before rising at higher fields \textemdash consistent with the emergence of single-phonon-induced resonant noise that becomes significant at sub-terahertz frequencies. These results establish $\mathrm{V_B^-}$ centers as a versatile platform for quantum sensing in the sub-terahertz, high-field regime.

Topological order (TO) provides a natural platform for storing and manipulating quantum information. However, its stability to noise has only been systematically understood for Abelian TOs. In this work, we exploit the non-deterministic fusion of non-Abelian anyons to inform active error correction and design decoders where the fusion products, instead of flag qubits, herald the noise. This intrinsic heralding enhances thresholds over those of Abelian counterparts when noise is dominated by a single non-Abelian anyon type. Furthermore, we use Bayesian inference to obtain a statistical mechanics model for fixed-point non-Abelian TOs with perfect measurements under any noise model, which yields the optimal threshold conditioned on measuring anyon syndromes. We numerically illustrate these results for $D_4 \cong \mathbb Z_4 \rtimes \mathbb Z_2$ TO. In particular, for non-Abelian charge noise and perfect syndrome measurement, we find a conditioned optimal threshold $p_c=0.218(1)$, whereas an intrinsically heralded minimal-weight perfect-matching (MWPM) decoder already gives $p_c=0.20842(2)$, outperforming standard MWPM with $p_c = 0.15860(1)$. Our work highlights how non-Abelian properties can enhance stability, rather than reduce it, and discusses potential generalizations for achieving fault tolerance.

The description of the entanglement dynamics of monitored non-interacting fermions, including the existence of measurement-induced phase transitions (MIPT), is a challenging problem with conflicting results in the literature. The mapping of the problem onto a non-linear sigma model (NLSM) indicates that relatively large lattice sizes are required to determine the nature of the entanglement entropy (EE) in the thermodynamics limit. Here we address this problem numerically for monitored non-interacting fermions with $U(1)$ symmetry. The use of Graphic-Processing-Unit (GPU) techniques, even with outdated hardware, makes possible to reach much larger lattice sizes ($L = 16384$ and $160\times160$ in one (1d) and two (2d) dimensions respectively) than in previous studies which enables us to characterize quantitatively the entanglement dynamics. In 1d, we show that in order to confirm the absence of a MIPT, for both projective and homodyne measurements, predicted by the NLSM it is necessary to reach $L \sim 10000$. In 2d, also as predicted by the NLSM, we observe for both protocols a MIPT at finite monitoring rate characterized by a scale invariant mutual information. The critical monitoring strength depends on the protocol while the critical exponent $\nu \approx 1.3$ governing the approach to the MIPT is similar in both cases. These features are not correctly predicted by the NLSM. Our results paves the way for a fully quantitative description of the entanglement dynamics of monitoring quantum systems.

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 develop a framework based on the Kirkwood-Dirac quasiprobability distribution to quantify the contribution of coherence to work extraction during generic, cyclic quantum evolutions. In particular, we focus on ``anomalous processes'', counterintuitive scenarios in which, due to the negativity of the quasiprobability distribution, work can be extracted even when individual processes are associated with energy gain. Applying this framework to qubits undergoing sequences of single- and two-qubit gate operations, we identify specific conditions under which such anomalous work exchanges occur. Furthermore, we analyze the quasiprobabilistic structure of deep quantum circuits and establish a compositional relation linking the work statistics of full circuits to those of their constituent gates. Our work highlights the role of coherence in the thermodynamics of quantum computation and provides a foundation for systematically studying potential thermodynamic relevance of specific quantum circuits.

Recently, proposals for realizing a nonreciprocal superradiant quantum phase transition (SQPT) have been put forward, based on either nonreciprocal interactions between two spin ensembles or the Sagnac-Fizeau shift in a spinning cavity. However, experimental implementation of such a nonreciprocal SQPT remains challenging. This motivates the search for new mechanisms capable of producing a nonreciprocal SQPT. Here, we propose an alternative approach to realize a nonreciprocal SQPT, induced by the magnon Kerr effect (MKE), in a cavity magnonic system, where magnons in a yttrium iron garnet (YIG) sphere are coupled to cavity photons. The MKE coefficient is positive ($K>0$) when the bias magnetic field is aligned along the crystallographic axis [100], but negative ($K<0$) when aligned along the axis [110]. We show that the steady-state phase diagram for $K > 0$ differs markedly from that for $K < 0$. This contrast is the origin of the nonreciprocal SQPT. By further studying the steady-state magnon occupation and its fluctuations versus the parametric drive strength, we demonstrate that the SQPT becomes nonreciprocal, characterized by distinct critical thresholds for $K > 0$ and $K < 0$. Moreover, we introduce a bidirectional contrast ratio to quantify this nonreciprocal behavior. Our work provides a new mechanism for realizing the nonreciprocal SQPT, with potential applications in designing nonreciprocal quantum devices.

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.

Routing is the task of permuting qubits in such a way that quantum operations can be parallelized maximally, given constraints on the hardware geometry. When simulating fermions in the Jordan-Wigner encoding with qubits, a one-dimensional nearest-neighbor-connected geometry is effectively imposed on the system, independently of the underlying hardware, which means that naively, an $O(N)$ depth routing overhead is incurred. Recently, Maskara et al. [arXiv:2509.08898] demonstrated that this routing overhead can be reduced to $O(\log N)$ by decomposing general fermion routing into $O(\log N)$ interleave permutations of depth $O(1)$, using $\Theta(N)$ ancillary qubits and employing measurements and feedforward. Here, we exhibit an alternative construction that achieves the same asymptotic performance. We also generalize the result in two ways. Firstly, we show that fermion routing can be performed in depth $O(\log^2 N)$ \emph{without} ancillas, measurements, or feedforward. Secondly, we construct efficient mappings with $O(\log^2 N)$ depth between all product-preserving ternary tree fermionic encodings, thereby showing that fermion routing in any such encoding can be done efficiently. While these results assume all-to-all connectivity, they also imply upper bounds for fermion routing in devices with limited connectivity by multiplying the fermion routing depth by the worst-case qubit routing depth.

Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline resource state generation. Prior work has primarily relied on the "logical gap" metric with the minimum-weight perfect matching decoder, but this approach faces fundamental limitations including computational overhead that scales exponentially with the number of logical qubits and poor generalizability to arbitrary codes beyond surface codes. We develop post-selection strategies based on computationally efficient heuristic confidence metrics that leverage error cluster statistics (specifically, aggregated cluster sizes and log-likelihood ratios) from clustering-based decoders, which are applicable to arbitrary quantum low-density parity check (QLDPC) codes. We validate our method through extensive numerical simulations on surface codes, bivariate bicycle codes, and hypergraph product codes, demonstrating orders of magnitude reductions in logical error rates with moderate abort rates. For instance, applying our strategy to the [[144, 12, 12]] bivariate bicycle code achieves approximately three orders of magnitude reduction in the logical error rate with an abort rate of only 1% (19%) at a physical error rate of 0.1% (0.3%). Additionally, we integrate our approach with the sliding-window framework for real-time decoding, featuring early mid-circuit abort decisions that eliminate unnecessary overheads. Notably, its performance matches or even surpasses the original strategy for global decoding, while exhibiting favorable scaling in the number of rounds. Our approach provides a practical foundation for efficient post-selection in fault-tolerant quantum computing with QLDPC codes.

The minimum weight matching (MWM) and maximum likelihood decoding (MLD) are two widely used and distinct decoding strategies for quantum error correction. For a given syndrome, the MWM decoder finds the most probable physical error corresponding to the MWM of the decoding graph, whereas MLD aims to find the most probable logical error. Although MLD is the optimal error correction strategy, it is typically more computationally expensive compared to the MWM decoder. In this work, we introduce an algorithm that approximates MLD with $K$ MWMs from the decoding graph. Taking the surface code subject to graphlike errors as an example, we show that it is possible to efficiently find the first $K$ MWMs by systematically modifying the original decoding graph followed by finding the MWMs of the modified graphs. For the case where the $X$ and $Z$ errors are correlated, despite the MWM of the decoding hypergraph cannot be found efficiently, we present a heuristic approach to approximate the MLD by finding the $K$ MWMs in the $X$ and $Z$ subgraphs. We benchmark the efficacy of our algorithm for the surface code subject to graphlike errors, the surface-square Gottesman-Kitaev-Preskill (GKP) code and surface-hexagonal GKP code subject to the Gaussian random displacement errors, showing that the fidelity approaches that of the exact MLD (for the first two cases) or the tensor-network decoder (for the last case) as $K$ increases.

Compilation and optimization of quantum circuits are critical components in the execution of algorithms on quantum computers. These components must successfully balance two competing priorities: minimizing the number of expensive resources, such as two-qubit gates or arbitrary angle single-qubit rotations, and minimizing the approximation error of the compiled circuit to the ideal target unitary describing the quantum algorithm. We develop a practical workflow for managing and optimizing this tradeoff, which enables quantum circuit compilation and optimization at scales of hundreds of qubits. Our workflow is able to tackle circuits at such large scales while providing rigorous guarantees on circuit output error by leveraging circuit partitioning and the notion of averaging over circuit ensembles. We demonstrate our workflow on several benchmark algorithmic circuits acting on up to 380 qubits, and show that it can simultaneously achieve substantial reductions in resource-intensive gates and control output errors, offering a practical and scalable strategy for both near-term and fault-tolerant quantum computing.

We show that space-time modulation of electromagnetic potentials enables Klein tunneling far below the static threshold. The derived kinematics reveal oblique transitions that can connect opposite-energy continua without requiring their overlap, yielding a velocity-tunable Klein gap where transmission vanishes within a finite velocity window and reemerges beyond. The associated reduction in energy thresholds -- by up to four orders of magnitude -- suggests the potential for experimental realization using flying-focus fronts and relativistic electron beams.

Object detection and range finding using a weak light source is vulnerable to jamming and spoofing attacks by an intruder. Quantum illumination with nonsimultaneous, phase-insensitive coincidence measurements can provide jamming resilience compared to identical measurements for classical illumination. We extend an experimentally-feasible object detection and range finding quantum illumination-based protocol to include spoofing resilience. This approach allows the system to be characterised by its experimental parameters and quantum states, rather than just its detector data. Therefore we can scope the parameter-space which provides some spoofing resilience without relying upon the prohibitive method of acquiring detector data for all combinations of the experimental parameters. We demonstrate that in certain regimes the intruder has an optimal relative detection basis angle to minimise the induced error. We also show that there are spoofing-vulnerable regimes where excessive background noise prevents any induced error, while it is still possible to perform object detection, i.e. our detectors have not been fully blinded. The sensing protocol which we describe can allow for the recognition of intrusion and the possible detection of our trustworthy return signal. Our results reinforce that quantum illumination is advantageous for spoofing resilience compared to a classical illumination-based protocol.

The nitrogen-vacancy (NV) center in diamond is a prime candidate for quantum sensing technologies. Here, we present a fully integrated and mechanically robust fiber-based endoscopic sensor with a tip diameter of $1.25 \mathrm{mm}$. On its tip, a direct laser writing process is used to fixate a diamond containing NV centers above the fiber's core inside a polymer structure. Additionally, a metallic direct laser-written antenna structure next to the fiber facet allows efficient microwave manipulation of NV center spins. The sensor achieves a shot-noise-limited magnetic-field sensitivity of $5.9 \mathrm{nT}/\sqrt{\mathrm{Hz}}$ using a $15 \mathrm{\mu m}$-sized microdiamond at a microwave power of $50 \mathrm{mW}$ and optical power of $2.15 \mathrm{mW}$. Using lock-in techniques, we measure a sensitivity of $51.8 \mathrm{nT}/\sqrt{\mathrm{Hz}}$. Furthermore, we introduce a dual-fiber concept that enables, in combination with a direct laser-written structure, independent guiding of excitation and fluorescence light and thus reduces background autofluorescence. Moreover, controlled guiding of excitation light to the diamond while avoiding sample illumination may enable operation in light-sensitive environments such as biological tissue. While the demonstrated sensitivity is achieved using a single-fiber configuration, the dual-fiber approach provides a path towards integrating smaller diamonds, where autofluorescence would otherwise limit performance. We demonstrate the capability of vector magnetic field measurements in a magnetic field as used in state-of-the-art ultracold quantum gas experiments, opening a potential field in which high resolution and high sensitivity are necessary.

The Fewster-Verch (FV) framework provides a local and covariant approach for defining measurements in quantum field theory (QFT). Within this framework, a probe QFT represents the measurement device, which, after interacting with the target QFT, undergoes an arbitrary local measurement. Remarkably, the FV framework is free from Sorkin-like causal paradoxes and robust enough to enable quantum state tomography. However, two open issues remain. First, it is unclear if the FV framework allows conducting arbitrary local measurements. Second, if the probe field is interpreted as physical and the FV framework as fundamental, then one must demand the probe measurement to be itself implementable within the framework. That would involve a new probe, which should also be subject to an FV measurement, and so on. It is unknown if there exist non-trivial FV measurements for which such an ``FV-Heisenberg cut" can be moved arbitrarily far away. In this work, we advance the first problem by proving that Gaussian-modulated measurements of locally smeared fields fit within the FV framework. We solve the second problem by showing that any such measurement admits a movable FV-Heisenberg cut. As a technical byproduct, we establish that state transformations induced by finite-rank perturbations of the classical phase space underlying a linear scalar field preserve the Hadamard property.

The coupling of two-level quantum systems to the thermal environment is a fundamental problem, with applications ranging from qubit state preparation to spin models. However, for the elementary problem of the thermodynamics of an ensemble of bosons populating a two-level system despite its conceptual simplicity experimental realizations are scarce. Using an optical dye microcavity platform, we thermalize photons in a two-mode system with tunable chemical potential, demonstrating N bosons populating a two-level system coupled to a heat bath. Under pulsed excitation, Josephson oscillations between the two quantum states demonstrate the possibility for coherent manipulation. In contrast, under stationary conditions the thermalization of the two-mode system is observed. As the energetic splitting between eigenstates is two orders of magnitude smaller than thermal energy, at low occupations an almost equal distribution of the modes occupation is observed, as expected from Boltzmann statistics. For larger occupation, we observe efficient population of the ground state and saturation of the upper level at high filling, expected from quantum statistics. Our experiment holds promise for state preparation in quantum technologies as well as for quantum thermodynamics studies.

For strongly correlated quantum systems, fundamental questions about the formation and stability of Floquet-Bloch sidebands (FBs) upon periodic driving remain unresolved. Here, we investigate the impact of electron-electron interactions and perturbations in the coherence of the driving on the lifetime of FBs by directly computing time-dependent single-particle spectral functions using exact diagonalization (ED) and matrix product states (MPS). We study interacting metallic and correlated insulating phases in a chain of correlated spinless fermions. At high-frequency driving we obtain clearly separated, long-lived FBs of the full many-body excitation continuum. However, if there is significant overlap of the features, which is more probable in the low-frequency regime, the interactions lead to strong heating, which results in a significant loss of quantum coherence and of the FBs. Similar suppression of FBs is obtained in the presence of noise. The emerging picture is further elucidated by the behavior of real-space single-particle propagators, of the energy gain, and of the momentum distribution function, which is related to a quantum Fisher information that is directly accessible by spectroscopic measurements.

We develop a systematic method for constructing asymptotic quantum many-body scar (AQMBS) states. While AQMBS states are closely related to quantum many-body scar (QMBS) states, they exhibit key differences. Unlike QMBS states, AQMBS states are not energy eigenstates of the Hamiltonian, making their construction more challenging. We demonstrate that, under appropriate conditions, AQMBS states can be obtained as low-lying gapless excited states of a parent Hamiltonian, which has a QMBS state as its ground state. Furthermore, our formalism reveals a connection between QMBS and supersymmetric (SUSY) quantum mechanics. The QMBS state can be interpreted as a SUSY-unbroken ground state.

We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This method allows us to generate well-behaved initial neural network quantum states for quantum many-body ground-state calculations in polynomial time of the number of variational parameters and systematically shorten the distance between the initial states and the ground states while increasing the rank of the CP decomposition. We demonstrate the efficiency of our method by taking the transverse-field Ising model as an example and discuss possible applications of our method to more general quantum many-body systems in which the ground-state wave functions possess complex nodal structures.

We study the local relaxation of closed quantum systems through the relative entropy between the reduced density matrix and its long time limit. We show, using analytic arguments combined with numerical checks, that this relative entropy can be very well approximated by an entropy difference, affording a significant computational advantage. We go on to relate this to the entanglement asymmetry of the subsystem with respect to time translation invariance. In doing this, we obtain a simple probe of the relaxation dynamics of closed many-body systems and use it to re-examine the quantum Mpemba effect, wherein states can relax faster if they are initially further from equilibrium. We reproduce earlier instances of the effect related to symmetry restoration as well as uncover new cases in the absence of such symmetries. For integrable models, we obtain the criteria for this to occur using the quasiparticle picture. Lastly, we show that, in models obeying the entanglement membrane picture, the quantum Mpemba effect cannot occur for a large class of initial states.

We examine the effective field theory (EFT) of maximal chaos through the lens of Krylov complexity and the Universal Operator Growth Hypothesis. We test the relationship between two measures of quantum chaos: out-of-time-ordered correlators (OTOCs) and Krylov complexity. In the EFT, a shift symmetry of the hydrodynamic modes enforces the maximal Lyapunov exponent in OTOCs, $\lambda_L = 2\pi T$, while simultaneously constraining thermal two-point autocorrelators. We solve these constraints on the autocorrelator, and calculate the Lanczos coefficients and Krylov exponents for several examples, finding both $\lambda_K = \lambda_L$ and $\lambda_K = \lambda_L/2$. This demonstrates that, within the EFT, the shift symmetry alone is insufficient to enforce maximal Krylov exponents even when the Lyapunov exponent is maximal. In particular, this result suggests a tension with the conjectured bound $\lambda_L \leq \lambda_K \leq 2\pi T$. Finally, we identify autocorrelator solutions whose power spectra closely resemble the so-called thermal product formula seen in holographic systems.

We prove a coordinate- and foliation-independent Heisenberg-type lower bound for quantum states strictly localized in geodesic balls of radius $r$ on spacelike hypersurfaces of arbitrary spacetimes (with matter and a cosmological constant). The estimate depends only on the induced Riemannian geometry of the slice; it is independent of the lapse, shift, and extrinsic curvature, and controls the canonical momentum variance/uncertainty $\sigma_p$ by the first Dirichlet eigenvalue of the Laplace-Beltrami operator (Theorem). On weakly mean-convex balls we obtain the universal product inequality $\sigma_p r \ge \hbar/2$. Under the same assumption, a vector-field Barta-type argument improves this universal floor to the scale-invariant bound $\sigma_p r \ge \pi\hbar/2$, which provides a universal, foliation-independent floor. Any further sharpening of the constant requires eigenvalue-comparison results or other curvature-sensitive methods.

In this paper, we investigate structural properties of finite groups that are detected by certain group invariants arising from Dijkgraaf--Witten theory, a topological quantum field theory, in one space and one time dimension. In this setting, each finite group $G$ determines a family of numerical invariants associated with closed orientable surfaces, expressed in terms of the degrees of the complex irreducible characters of $G$. These invariants can be viewed as natural extensions of the commuting probability $d(G)$, which measures the likelihood that two randomly chosen elements of $G$ commute and has been extensively studied in the literature. By analyzing these higher-genus analogues, we establish new quantitative criteria relating the values of these invariants to key structural features of finite groups, such as commutativity, nilpotency, supersolvability and solvability. Our results generalize several classical theorems concerning the commuting probability, thereby linking ideas from finite group theory and topological quantum field theory.

In these notes the Born series for the $s$-wave scattering $a_0$ is calculated for a class of central potentials $V(r)$ up to sixth order in a dimensionless coupling strength $g$. Examples of exponentially decaying potentials as well truncated potentials involving a single length-scale $a$ are considered. In certain favorable cases the exact result for the $g$-dependent $s$-wave scattering length $a_0=A_0(g) a$ can be given in terms of special functions. The poles of $A_0(g)$ at increasing positive values of $g$ correspond to the thresholds, where $s$-wave bound-states occur successively. A scattering problem, where $A_0(g)$ is solvable in terms of elementary functions, is also presented.