The rapid advancements in quantum computing (QC) and machine learning (ML) have led to the emergence of quantum machine learning (QML), which integrates the strengths of both fields. Among QML approaches, variational quantum circuits (VQCs), also known as quantum neural networks (QNNs), have shown promise both empirically and theoretically. However, their broader adoption is hindered by reliance on quantum hardware during inference. Hardware imperfections and limited access to quantum devices pose practical challenges. To address this, the Quantum-Train (QT) framework leverages the exponential scaling of quantum amplitudes to generate classical neural network parameters, enabling inference without quantum hardware and achieving significant parameter compression. Yet, designing effective quantum circuit architectures for such quantum-enhanced neural programmers remains non-trivial and often requires expertise in quantum information science. In this paper, we propose an automated solution using differentiable optimization. Our method jointly optimizes both conventional circuit parameters and architectural parameters in an end-to-end manner via automatic differentiation. We evaluate the proposed framework on classification, time-series prediction, and reinforcement learning tasks. Simulation results show that our method matches or outperforms manually designed QNN architectures. This work offers a scalable and automated pathway for designing QNNs that can generate classical neural network parameters across diverse applications.

We investigate the structure and uniqueness of squeezed vacuum states defined by annihilation conditions of the form $(a - \alpha a^\dagger)|\psi\rangle = 0$ and their multimode generalizations. For $N=1$ and $N=2$, we rigorously show that these conditions uniquely define the standard single- and two-mode squeezed states in the Fock basis. We then analyze a cyclically coupled $N$-mode system governed by $(a_i - \alpha_i a_{i+1}^\dagger)|\psi\rangle = 0$ with $a_{N+1} \equiv a_1$. Although the recurrence structure restricts solutions to equal-photon-number states, we prove that for $N>2$ no such state satisfies the full set of conditions. This establishes a sharp no-go result for multipartite squeezed states under cyclic annihilation constraints, underscoring a fundamental structural limitation beyond pairwise squeezing.

Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale, fault-tolerant quantum computers a prominent challenge. To combat errors, pioneering experiments have demonstrated a variety of quantum error correction codes. Yet, most of these codes suffer from low encoding efficiency, and their scalability is hindered by prohibitively high resource overheads. Here, we report the demonstration of two low-overhead quantum low-density parity-check (qLDPC) codes, a distance-4 bivariate bicycle code and a distance-3 qLDPC code, on our latest superconducting processor, Kunlun, featuring 32 long-range-coupled transmon qubits. Utilizing a two-dimensional architecture with overlapping long-range couplers, we demonstrate simultaneous measurements of all nonlocal weight-6 stabilizers via the periodic execution of an efficient syndrome extraction circuit. We achieve a logical error rate per logical qubit per cycle of $(8.91 \pm 0.17)\%$ for the distance-4 bivariate bicycle code with four logical qubits and $(7.77 \pm 0.12)\%$ for the distance-3 qLDPC code with six logical qubits. Our results establish the feasibility of implementing various qLDPC codes with long-range coupled superconducting processors, marking a crucial step towards large-scale low-overhead quantum error correction.

High-fidelity logical magic states are a critical resource for fault-tolerant quantum computation, enabling non-Clifford logical operations through state injection. However, benchmarking these states presents significant challenges: one must estimate the infidelity $\epsilon$ with multiplicative precision, while many quantum error-correcting codes only permit Clifford operations to be implemented fault-tolerantly. Consequently, conventional state tomography requires $\sim1/\epsilon^2$ samples, making benchmarking impractical for high-fidelity states. In this work, we show that any benchmarking scheme measuring one copy of the magic state per round necessarily requires $\Omega(1/\epsilon^2)$ samples for single-qubit magic states. We then propose two approaches to overcome this limitation: (i) Bell measurements on two copies of the twirled state and (ii) single-copy schemes leveraging twirled multi-qubit magic states. Both benchmarking schemes utilize measurements with stabilizer states orthogonal to the ideal magic state and we show that $O(1/\epsilon)$ sample complexity is achieved, which we prove to be optimal. Finally, we demonstrate the robustness of our protocols through numerical simulations under realistic noise models, confirming that their advantage persists even at moderate error rates currently achievable in state-of-the-art experiments.

Quantum dots are promising candidates for deterministic single-photon sources, yet achieving high photon indistinguishability at telecom wavelengths remains a critical challenge. Here, we report a quantum dot-based single-photon source operating in the telecommunications C-band that achieves a raw two-photon interference visibility of up to (91.7+-0.2)%, thus setting a new benchmark for indistinguishability in this spectral range. The device consists of an indium arsenide (InAs) quantum dot embedded within indium aluminum gallium arsenide (InAlGaAs) and integrated into a circular Bragg grating resonator. We explore multiple optical excitation schemes to optimize coherence and source performance. To our knowledge, this is the first demonstration of two-photon interference visibility exceeding 90% from a quantum-dot emitter in the telecommunications C-band, advancing the viability of solid-state sources for quantum communication and photonic networks.

Complex quantum systems -- composed of many, interacting particles -- are intrinsically difficult to model. When a quantum many-body system is subject to disorder, it can undergo transitions to regimes with varying non-ergodic and localized behavior, which can significantly reduce the number of relevant basis states. It remains an open question whether such transitions are also directly related to an abrupt change in the system's complexity. In this work, we study the transition from chaotic to integrable phases in several paradigmatic models, the power-law random banded matrix model, the Rosenzweig--Porter model, and a hybrid SYK+Ising model, comparing three complementary complexity markers -- fractal dimension, von Neumann entanglement entropy, and stabilizer R\'enyi entropy. For all three markers, finite-size scaling reveals sharp transitions between high- and low-complexity regimes, which, however, can occur at different critical points. As a consequence, while in the ergodic and localized regimes the markers align, they diverge significantly in the presence of an intermediate fractal phase. Additionally, our analysis reveals that the stabilizer R\'enyi entropy is more sensitive to underlying many-body symmetries, such as fermion parity and time reversal, than the other markers. As our results show, different markers capture complementary facets of complexity, making it necessary to combine them to obtain a comprehensive diagnosis of phase transitions. The divergence between different complexity markers also has significant consequences for the classical simulability of chaotic many-body systems.

The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques - such as Matrix Product States (MPS) - when computing time-dependent expectation values. This entanglement barrier restricts classical simulations and, conversely, underpins the quantum advantage anticipated from future devices. Here we show that, for one-dimensional Hamiltonian dynamics, the spatio-temporal tensor network encoding the evolved wave-function amplitudes can be contracted efficiently along the left-right (spatial) direction. Exploiting this structure, we develop a hybrid Tensor-Network/Monte-Carlo (TN-MC) algorithm that samples the wave function and evaluates expectation values of generic local operators with computational cost that scales only polynomially in time. We benchmark the method on the chaotic transverse-field Ising chain. By tracking the time dependence of the generalised temporal entropies governing the TN contraction, we find that their real part either saturates or grows logarithmically with time, revealing new instances of continuous dynamical quantum phase transitions (DQPTs). Our results therefore place the claim that the entanglement barrier can be bypassed with a TN-MC blend on firm theoretical footing.

The amazing quantum effect of `entanglement' was discovered in the 1935 thought experiment by Albert Einstein, Boris Podolsky and Nathan Rosen (`EPR'). The ensuing research opened up fundamental questions and led to experiments that proved that quantum theory cannot be completed by local hidden variables. Remarkably, EPR did not discuss how to create the entanglement in their thought experiment. Here I add this part. What is required in the original EPR thought experiment is a simple elastic particle collision, an unbalanced mass ratio of e.g. 1:3 and initial states that are position and momentum squeezed, respectively. In the limiting case of infinite squeeze factors, the measurement of the position or momentum of one particle allows an absolutely precise conclusion to be drawn about the value of the same quantity of the other particle. The EPR idea has never been tested in this way. I outline a way to do this.

We propose a quantum algorithm, inspired by ADAPT-VQE, to variationally prepare the ground state of a quantum Hamiltonian, with the desirable property that if it fails to find the ground state, it still yields a physically meaningful local-minimum state that oftentimes corresponds to a metastable state of the quantum system. At each iteration, our algorithm reduces the energy using a set of local physical operations. The operations to perform are chosen using gradient and Hessian information that can be efficiently extracted from experiments. We show that our algorithm does not suffer from the barren plateau problem, which is a significant issue in many variational quantum algorithms. We use numerical simulation to demonstrate that our method reliably produces either the true ground state or a physically meaningful metastable state in typical physical systems with such states.

Efficient simulation of a quantum system generally relies on structural properties of the quantum state. Motivated by the recent results by Bakshi et al. on the sudden death of entanglement in high-temperature Gibbs states of quantum spin systems, we study the high-temperature Gibbs states of bounded-degree local fermionic Hamiltonians, which include the special case of geometrically local fermionic systems. We prove that at a sufficiently high temperature that is independent of the system size, the Gibbs state is a probabilistic mixture of fermionic Gaussian states. This forms the basis of an efficient classical algorithm to prepare the Gibbs state by sampling from a distribution of fermionic Gaussian states.

The Quantum Fisher Information Matrix (QFIM) is a fundamental quantity in various subfields of quantum physics. It plays a crucial role in the study of parameterized quantum states, as it quantifies their sensitivity to variations in its parameters. Recently, the QFIM has been successfully employed to enhance the optimization of variational quantum algorithms. However, its practical applicability is often hindered by the high resource requirements for its estimation. In this work, we introduce a novel protocol for computing the off-block-diagonal elements of the QFIM between different layers in a particular class of variational quantum circuits, known as commuting-block circuits. Our approach significantly reduces the quantum resources required, specifically lowering the number of distinct quantum state preparations from $O(m^2)$ to $O(L^2)$, where $m$ is the total number of parameters and $L$ is the number of layers in the circuit. Consequently, our protocol also minimizes the number of classical measurements and post-processing operations needed to estimate the QFIM, leading to a substantial improvement in computational efficiency.

We propose a constructive and dynamical redefinition of spatial structure, grounded in the interplay between mechanical evolution and observational acts. Rather than presupposing space as a static background, we interpret space as an emergent entity that arises through observational acts. Using the framework of pre-topologies, measurable structures, and the GNS construction, we analyze how the choice of observables and the system's time evolution dynamically determine the topological and measure-theoretic features of space. This approach highlights the observer-dependent and context-sensitive nature of spatial concepts in both classical and quantum domains.

Levitation in vacuum of macroscopic objects is key towards the development of novel types of inertial sensors and pressure sensors, as well as towards the fundamental studies of quantum mechanics and its relation to gravity. Diamagnetic levitation offers a passive method at room temperature to isolate macroscopic objects in vacuum environments, yet eddy current damping remains a critical limitation for electrically conductive materials. We show that there are situations where the motion of conductors in magnetic fields do not, in principal, produce eddy damping, and demonstrate an electrically conducting rotor diamagnetically levitated in an axially symmetric magnetic field in high vacuum. Experimental measurements and finite-element simulations reveal gas collision damping as the dominant loss mechanism at high pressures, while residual eddy damping, which arises from symmetry-breaking factors such as platform tilt or material imperfections, dominates at low pressures. This demonstrates a macroscopic levitated rotor with extremely low rotational damping, and paves the way to fully suppress rotor damping, enabling ultra-low-loss rotors for gyroscopes, pressure sensing, and fundamental physics tests.

The Sachdev--Ye--Kitaev (SYK) model may provide us with a good starting point for the experimental study of quantum chaos and holography in the laboratory. Still, the four-local interaction of fermions makes quantum simulation challenging, and it would be good to search for simpler models that keep the essence. In this paper, we argue that the four-local interaction may not be important by introducing a few models that have two-local interactions. The first model is a generalization of the spin-SYK model, which is obtained by replacing the spin variables with SU($d$) generators. Simulations of this class of models might be straightforward on qudit-based quantum devices. We study the case of $d=3, 4, 5, 6$ numerically and observe quantum chaos already for two-local interactions in a wide energy range. We also introduce modifications of spin-SYK and SYK models that have similar structures to the SU($d$) model (e.g., $H=\sum_{p,q}J_{pq}\chi_p\chi_{p+1}\chi_q\chi_{q+1}$ instead of the original SYK Hamiltonian $H=\sum_{p,q,r,s}J_{pqrs}\chi_p\chi_q\chi_r\chi_{s}$), which shows strongly chaotic features although the interaction is essentially two-local. These models may be a good starting point for the quantum simulation of the original SYK model.

We introduce the coherent-incoherent correspondence as a framework for deriving quantum thermodynamic uncertainty relations under continuous measurement in Lindblad dynamics. The coherent-incoherent correspondence establishes a mapping between the original quantum system with coherent evolution and a corresponding incoherent system without coherent dynamics. The coherent-incoherent correspondence relates quantities across these two systems, including jump statistics, dynamical activity, and entropy production. Since the classical-like properties of the incoherent system allow us to derive thermodynamic uncertainty relations in the incoherent system, we can transfer the relations from the incoherent to the coherent system via the coherent-incoherent correspondence. This enables the derivation of quantum thermodynamic uncertainty relations for the original coherent system. Unlike existing quantum uncertainty relations, which typically include explicit quantum correction terms, our approach avoids these additional terms. This framework provides a general approach to deriving trade-offs in quantum thermodynamics.

In order to explore the possibility of cross-fertilization between quantum computing and neural networks as well as to improve the classification performance of quantum neural networks, this paper proposes an improved Variable Split Shadow Quantum Circuit (VSQC-WOA) model based on the Whale Optimization Algorithm. In this model, we design a strongly entangled local shadow circuit to achieve efficient characterization of global features through local shadow feature extraction and a sliding mechanism, which provides a rich quantum feature representation for the classification task. The gradient is then computed by the parameter-shifting method, and finally the features processed by the shadow circuit are passed to the classical fully connected neural network (FCNN) for processing and classification. The model also introduces the Whale Optimization Algorithm (WOA) to further optimize the weights and biases of the fully connected neural network, which improves the expressive power and classification accuracy of the model. In this paper, we firstly use different localized shadow circuit VSQC models to achieve the binary classification task on the MNIST dataset, and our design of strongly entangled shadow circuits performs the best in terms of classification accuracy. The VSQC-WOA model is then used to multi-classify the MNIST dataset (three classifications as an example), and the effectiveness of the proposed VSQC-WOA model as well as the robustness and generalization ability of the model are verified through various comparison experiments.

Recent advances in artificial intelligence (AI) and quantum computing are accelerating automation in scientific and engineering processes, fundamentally reshaping research methodologies. This perspective highlights parallels between scientific automation and established Computer-Aided Engineering (CAE) practices, introducing Quantum CAE as a framework that leverages quantum algorithms for simulation, optimization, and machine learning within engineering design. Practical implementations of Quantum CAE are illustrated through case studies for combinatorial optimization problems. Further discussions include advancements toward higher automation levels, highlighting the critical role of specialized AI agents proficient in quantum algorithm design. The integration of quantum computing with AI raises significant questions about the collaborative dynamics among human scientists and engineers, AI systems, and quantum computational resources, underscoring a transformative future for automated discovery and innovation.

Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of high-dimensional quantum technology, a significant effort is underway to progressively enhance the entanglement dimension between two particles. An alternative effective strategy involves not only increasing the dimensionality but also expanding the number of particles that are entangled. We present an experimental study demonstrating multi-partite quantum non-locality beyond qubit constraints, thus moving into the realm of strongly entangled high-dimensional multi-particle quantum systems. In the experiment, quantum states were encoded in the path degree of freedom (DoF) and controlled via polarization, enabling efficient operations in a two-dimensional plane to prepare three- and four-particle Greenberger-Horne-Zeilinger (GHZ) states in three-level systems. Our experimental results reveal ways in which high-dimensional systems can surpass qubits in terms of violating local-hidden-variable theories. Our realization of multiple complex and high-quality entanglement technologies is an important primary step for more complex quantum computing and communication protocols.

The discrimination between non-orthogonal quantum states plays a pivotal role in quantum information processing and quantum technology. Strategies that minimize the error probability are of particular importance, but they are only known for special classes of problems. Certain forms of Fano's inequality yield a bound on the error probability, but it is not known how close this bound is to the minimum-error probability achieved by means of optimal measurements. In this work we discuss how the minimum-error probability compares to the error bound obtained through the Fano's inequality for several scenarios, some of which are amenable to analytic treatments.

We introduce a class of thermal operations based on the collision model, where the system sequentially interacts with uncorrelated bath molecules via energy-preserving unitaries. To ensure finite complexity, each molecule is constrained to be no larger than the system. We identify a necessary condition for cooling below the bath temperature via a single collision: the system must initially lack a well-defined effective temperature, even a negative one. By constructing a iterative protocol, we demonstrate that sub-bath cooling is achievable without a machine under these restricted thermal operations. Moreover, introducing a qubit machine further enhances both the cooling limit and energy efficiency. These findings contribute to the broader study of cooling with finite resources.

Quantum reservoir computing (QRC) is an emerging framework for near-term quantum machine learning that offers in-memory processing, platform versatility across analogue and digital systems, and avoids typical trainability challenges such as barren plateaus and local minima. The exponential number of independent features of quantum reservoirs opens the way to a potential performance improvement compared to classical settings. However, this exponential scaling can be hindered by exponential concentration, where finite-ensemble noise in quantum measurements requires exponentially many samples to extract meaningful outputs, a common issue in quantum machine learning. In this work, we go beyond static quantum machine learning tasks and address concentration in QRC for time-series processing using quantum-scrambling reservoirs. Beyond discussing how concentration effects can constrain QRC performance, we demonstrate that leveraging Hamiltonian symmetries significantly suppresses concentration, enabling robust and scalable QRC implementations. The proposed strategy is illustrated in examples, including a well-known QRC design.

Scrambling quantum systems have been demonstrated as effective substrates for temporal information processing. While their role in providing rich feature maps has been widely studied, a theoretical understanding of their performance in temporal tasks is still lacking. Here we consider a general quantum reservoir processing framework that captures a broad range of physical computing models with quantum systems. We examine the scalability and memory retention of the model with scrambling reservoirs modelled by high-order unitary designs in both noiseless and noisy settings. In the former regime, we show that measurement readouts become exponentially concentrated with increasing reservoir size, yet strikingly do not worsen with the reservoir iterations. Thus, while repeatedly reusing a small scrambling reservoir with quantum data might be viable, scaling up the problem size deteriorates generalization unless one can afford an exponential shot overhead. In contrast, the memory of early inputs and initial states decays exponentially in both reservoir size and reservoir iterations. In the noisy regime, we also prove exponential memory decays with iterations for local noisy channels. Proving these results required us to introduce new proof techniques for bounding concentration in temporal quantum learning models.

Recent years have enjoyed a strong interest in exploring properties and applications of random quantum circuits. In this work, we explore the ensemble of $t$-doped Clifford circuits on $n$ qubits, consisting of Clifford circuits interspersed with $t$ single-qubit non-Clifford gates. We establish rigorous convergence bounds towards unitary $k$-designs, revealing the intrinsic cost in terms of non-Clifford resources in various flavors. First, we analyze the $k$-th order frame potential, which quantifies how well the ensemble of doped Clifford circuits is spread within the unitary group. We prove that a quadratic doping level, $t = \tilde{\Theta}(k^2)$, is both necessary and sufficient to approximate the frame potential of the full unitary group. As a consequence, we refine existing upper bounds on the convergence of the ensemble towards state $k$-designs. Second, we derive tight bounds on the convergence of $t$-doped Clifford circuits towards relative-error $k$-designs, showing that $t = \tilde{\Theta}(nk)$ is both necessary and sufficient for the ensemble to form a relative $\varepsilon$-approximate $k$-design. Similarly, $t = \tilde{\Theta}(n)$ is required to generate pseudo-random unitaries. All these results highlight that generating random unitaries is extremely costly in terms of non-Clifford resources, and that such ensembles fundamentally lie beyond the classical simulability barrier. Additionally, we introduce doped-Clifford Weingarten functions to derive analytic expressions for the twirling operator over the ensemble of random doped Clifford circuits, and we establish their asymptotic behavior in relevant regimes.

Optical cavities can be used to enhance the interaction of light with atoms or molecules. In a regime where cavity resonances are very far from the atomic or molecular transition frequencies, photon absorption can be neglected and the dispersive part of the interaction can induce spectacular phenomena such as squeezing, cooling, and self-organization. So far, this dispersive interaction regime has only been explored using a single or few longitudinal cavity modes at a time. We experimentally study the dispersive interaction between a cold atom cloud and many longitudinal modes of a Fabry-Perot cavity, by detecting collective light shifts in the transmission spectrum of an optical frequency comb probe. Notably, using a high quality resonator coupled to more than $10^5$ intracavity atoms, we detect appreciable shifts of $\sim 100$ cavity modes simultaneously. These results constitute a direct demonstration of dispersive coupling of matter with many longitudinal modes of a linear resonator, and pave the way towards deeper exploration of atom-light dynamics in the multifrequency domain.

Light-matter interactions with quantum dots have been extensively studied to harness key quantum properties of photons, such as indistinguishability and entanglement. In this theoretical work, we exploit the atomic-like four-level structure of a quantum dot coupled to a waveguide to model a shaping frequency entangling gate (ShaFrEnGa) for single photons. Our approach is based on the identification of input frequencies and an atomic level structure for which frequency-dependent one-photon transitions are adiabatically eliminated, while frequency-dependent two-photon transitions are resonantly enhanced. The frequency entanglement performance of the gate is analyzed using a Schmidt decomposition for continuous variables, revealing a trade-off between entanglement generation efficiency and entanglement quality. We further demonstrate the use of the ShaFrEnGa for the generation of entangled frequency qudit states.

The mixing of scalar substances in fluid flows by stirring and diffusion is ubiquitous in natural flows, chemical engineering, and microfluidic drug delivery. Here, we present a spectral quantum algorithm for scalar mixing by solving the advection-diffusion equation in a quantum computational fluid dynamics framework. We derive exact gate decompositions of the advection and diffusion operators in spectral space. For all but the simplest one-dimensional flows, these operators do not commute. Therefore, we use operator splitting and construct quantum circuits capable of simulating arbitrary polynomial velocity profiles, such as the Blasius profile of a laminar boundary layer. Periodic, Neumann, and Dirichlet boundary conditions can be imposed with the appropriate quantum spectral transform plus additional constraints on the Fourier expansion. We evaluate our approach in statevector simulations of a Couette flow, plane Poiseuille flow, and a polynomial Blasius profile approximation to demonstrate its potential and versatility for scalar mixing in shear flows. The number of gates grows with, at most, the cubed logarithm of the number of grid points. This evaluation shows that spectral accuracy allows comparably large time steps even though the operator splitting limits the temporal order.

Quantum network sensing shows potential to enhance the estimation precision for functions of spatially distributed parameters beyond the shot noise limit. The key resource required for this task is possibly multi-partite quantum entanglement. The photonic entanglement is the most natural for this task; however, distributing it over long distances presents significant difficulties, mainly because of unavoidable loss in communication channels. In this research, we analyze a quantum network sensing protocol based on a recently proposed, efficient GHZ state distribution scheme. In comparison to conventional methods based on entanglement distribution , our protocol shows the decreasing loss-induced estimation error of certain functions of distributed parameters including their arbitrary linear combinations.

We propose a low-pass-filter (LPF) feedback control for cooling a trapped particle with a low-pass filter, and show that it can achieve the minimum phonon occupation number lower than cold damping and linear-quadratic-Gaussian (LQG) control, which are the standard methods of ground-state cooling of a levitated nanoparticle. For the detection efficiency of $90\%$, the achievable phonon occupation number with our LPF control is about one third and a half of that of cold damping and LQG control, respectively, and thus our method has a decisive advantage to reach the absolute ground state.

This paper explores multiparameter quantum metrology using Greenberger-Horne-Zeilinger (GHZ)-type photon-added coherent states (PACS) and investigates both independent and simultaneous parameter estimation with linear and non-linear protocols, highlighting the significant potential of quantum resources to enhance precision in multiparameter scenarios. To provide a comprehensive analysis, we explicitly derive analytical expressions for the quantum Cram\'er-Rao bound (QCRB) for each protocol. Additionally, we compare the two estimation strategies, examining the behavior of their QCRBs and offering insights into the advantages and limitations of these quantum states in various contexts. Our results show that simultaneous estimation generally outperforms independent estimation, particularly in non-linear protocols. Furthermore, we analyze how the QCRB varies with the coherent state amplitude $|\alpha|^2$, the number of estimated parameters $d$, and the photon excitation order $n$ across three protocols. The results indicate that increasing $|\alpha|^2$ and decreasing $d$ improves estimation precision. For low $n$, the variation in the QCRB is similar for both symmetric and antisymmetric cases; however, at higher $n$, the antisymmetric case exhibits slightly better precision. The dependence on $d$ is comparable for both types of states. We also compare PACS-based GHZ states with NOON states and entangled coherent states, demonstrating the relative performance of each. Finally, we conclude with an analysis of homodyne detection in the context of a linear protocol, discussing its impact on estimation accuracy.

Local automaton decoders offer a promising path toward real-time quantum error correction by replacing centralized classical decoding, with inherent hardware constraints, by a natively parallel and streamlined architecture from a simple local transition rule. We propose two new types of local decoders for the quantum repetition code in one dimension. The signal-rule decoders interpret odd parities between neighboring qubits as defects, attracted to each other via the exchange of classical point-like excitations, represented by a few bits of local memory. We prove the existence of a threshold in the code-capacity model and present numerical evidence of exponential logical error suppression under a phenomenological noise model, with data and measurement errors at each error correction cycle. Compared to previously known local decoders that suffer from sub-optimal threshold and scaling, our construction significantly narrows the gap with global decoders for practical system sizes and error rates. Implementation requirements can be further reduced by eliminating the need for local classical memories, with a new rule defined on two rows of qubits. This shearing-rule works well at relevant system sizes making it an appealing short-term solution. When combined with biased-noise qubits, such as cat qubits, these decoders enable a fully local quantum memory in one dimension.

We introduce a device-independent quantum key distribution protocol for N parties, using the multipartite Hardy paradox to certify genuine multipartite nonlocality. Unlike traditional multipartite protocols that extract the key from measurement outcomes, our approach generates the shared secret key directly from the parties' choices of measurement settings. This settings-based method, certified by the maximal violation of the multipartite Hardy paradox, achieves a positive key rate and offers a fresh perspective on secure key distribution. Notably, the Hardy paradox enables any two parties to create a secret key with a rate much higher than the N-party key, due to more robust pairwise correlations. This unique capability, inherent to the multipartite Hardy paradox, allows for tailored key distribution within the group, enhancing flexibility. Our work establishes a new paradigm for device-independent conference key agreement, where keys are generated directly from measurement settings using non-maximally entangled states. This approach ensures robust security in untrusted quantum networks and enables pairwise key rates that surpass the N-party rate, offering unprecedented flexibility in key distribution. By challenging conventional methods, it paves the way for scalable, noise-resilient multiparty quantum communication systems.

In this work, we reassess our previous hybrid semiclassical gravity model and demonstrate its ability to induce entanglement even in the limit of weak entanglement. By incorporating feedback terms sourced from gravitational potential interactions between subsystems, based on a refined version of Theory of (Exclusively) Local Beables developed by Travis Norsen, we show that these interactions alone can generate entanglement. Building on this insight, we propose a novel communication scheme and introduce the concept of dynamical equilibrium, which formalizes a stable strategy for subsystems. This framework is inspired by the quantum equilibrium hypothesis of de Broglie Bohm theory and causal interpretation of David Bohm and Jean Pierre Vigier.

A universal quantum computer~(QC), though promising ground breaking solutions to complex problems, still faces several challenges with respect to scalability. Current state-of-the-art QC use a great quantity of cables to connect the physical qubits, situated in the cryogenic temperature, to room temperature electronics. Integrated cryogenic electronics together with semiconductor spin qubits is one way closer for scalability. Such a scalable quantum computer can have qubits and the control electronics at 4K stage. Being at 4K, more thermal dissipation is allowed without overloading the cooling capability of the fridge. Still, control and power circuitry is expected to be highly efficient. While commercial CMOS technologies are found to be operatable at \qty{}{mK}, lack of reliable cryogenic models while designing, increased mismatches at cryo temperatures makes the design challenging and risky. Using an FDSOI technology with backgate biasing to compensate for the threshold voltage drift happening at cryo~(compensating around 200mV) and digital circuitry is a way to address this challenge. In this work, a self-clocked digital low dropout regulator (DLDO) is designed in FDSOI for high power efficient, variation tolerant regulator to supply cryogenic circuits for Quantum computing. The proposed digital LDO is more resilient to mismatch and having self clocking and close and fine loops addresses the power efficiency and faster transient response.

We investigate global locations of Schmidt number witnesses which are outside of the convex set of all bi-partite states. Their locations are classified by interiors of faces of the convex set of all states, by considering the line segments from them to the maximally mixed state. In this way, a nonpositive Hermitian matrix of trace one is located outside of one and only one face. Faces of the convex set of all states are classified by subspaces, which are range spaces of states belonging to specific faces. For a given subspace, we show that there exist Schmidt number $k+1$ witnesses outside of the face arising from this subspace if and only if every vector in the orthogonal complement of the subspace has Schmidt rank greater than $k$. Once we have Schmidt number $k+1$ witnesses outside of a face, we also have Schmidt number $2,3,\dots, k$ witnesses outside of the face.

With the increasing demand for ultra-precise time synchronization and frequency dissemination across various scientific, industrial, and communication fields, the Czech Republic has developed an innovative, non-commercial fiber-based infrastructure. This infrastructure serves as a shared platform, utilizing optical fibers to enable high-precision timing, coherent frequency transfer, and a newly implemented vibrational sensing capability. The project also addresses challenges posed by classical communication noise-particularly from Raman scattering-on quantum channels, especially for Quantum Key Distribution (QKD). By strategically separating classical and quantum channels into distinct wavelength bands, such as the C-band and O-band, the infrastructure achieves minimal interference while enabling multiple concurrent applications over shared fiber lines.

The Dicke model, renowned for its superradiant quantum phase transition (QPT), also exhibits a transition from regular to chaotic dynamics. In this work, we provide a systematic, comparative study of static and dynamical indicators of chaos for the closed and open Dicke model. In the closed Dicke model, we find that indicators of chaos sensitive to long-range correlations in the energy spectrum such as the the spectral form factor can deviate from the Poissonian random matrix theory (RMT) predictions and show a dip-ramp-plateau feature even in the normal region of the Dicke model unless very large values of the spin size are chosen. Thus, care is needed in using such indicators of chaos. In the open Dicke model with cavity damping, we find that the dissipative spectral form factor emerges as a robust diagnostic displaying a quadratic dip-ramp-plateau behavior in agreement with the Ginebre Unitary Ensemble (GinUE) RMT in the superradiant regime. Moreover, by examining the spectral properties of the Liouvillian, we provide indirect evidence for the concurrence of the dissipative superradiant quantum phase transition and the change in Liouvillian eigenvalue statistics from 2-D Poissonian to GinUE RMT behavior.

Quantum frequency conversion serves a key role in the realization of hybrid quantum networks by interfacing between wavelength-incompatible platforms. Here we present the first quantum frequency converter connecting visible and telecom domains on a silicon nitride (SiN) chip, using Bragg-scattering four-wave mixing to upconvert heralded single photons from 1260 to 698 nm, which covers a 192 THz span. We examine the noise sources in SiN and devise approaches to suppress noise photons at the source and target frequencies to enable measurements at the single-photon level. We demonstrate an on-chip conversion efficiency of 5% in photon flux and describe design modifications that can be implemented to significantly improve it. Our results pave the way for the implementation of CMOS-compatible devices in quantum networks.

Periodically driven Floquet quantum systems hold great promise for engineering exotic quantum phases and matter, but are often hindered by thermalization. In this work, we propose and demonstrate a square wave modulated Floquet engineering protocol to steer and study thermalization dynamics in one dimensional Rydberg atom arrays. We identify a novel reciprocal Floquet thermalization mechanism, which is triggered when combination of laser detuning and the Rydberg atom interaction and Floquet period are reciprocal pairs. This leads to many-body quantum chaos, evidenced by level spacing distribution of the Floquet operator. Signatures of the thermalization can be found from stroboscopic evolution of the atom population, which saturates to that of the thermal ensemble state. Critically, the thermalization occurs in the disorder-free regime, with rapid equilibration achieved within the Rydberg lifetime and experimentally accessible initial states. Our study establishes a robust framework for manipulating out-of-equilibrium dynamics in many-body interacting spin systems. This approach opens pathways for exploring thermalization-to-localization transitions and designing effective Hamiltonians, and highlight the unique potential of the Rydberg atom array setting for quantum simulation.

An efficient paradigm for multi-party computation (MPC) are protocols structured around access to shared pre-processed computational resources. In this model, certain forms of correlated randomness are distributed to the participants prior to their computation. The shared randomness is then consumed in a computation phase that involves public communication with efficient round complexity, and the computation is secure in this second phase provided the initial correlations were distributed securely. Usually the latter requires some strong setup assumptions, such as a trusted dealer and private channels. We present a novel approach for generating these correlations from entangled quantum graph states and yield information-theoretic privacy guarantees that hold against a malicious adversary, with limited assumptions. Our primary contribution is a tripartite resource state and measurement-based protocol for extracting a binary multiplication triple, a special form of shared randomness that enables the private multiplication of a bit conjunction. Here, we employ a third party as a Referee and demand only an honest pair among the three parties. The role of this Referee is weaker than that of a Dealer, as the Referee learns nothing about the underlying shared randomness that is disseminated. We prove perfect privacy for our protocol, assuming access to an ideal copy of the resource state, an assumption that is based on the existence of graph state verification protocols. Finally, we demonstrate its application as a primitive for more complex Boolean functionalities such as 1-out-of-2 oblivious transfer (OT) and MPC for an arbitrary $N$-party Boolean function, assuming access to the proper broadcasting channel.

We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these may be used to prepare entangled logical states such as Bell pairs or GHZ states. This bears some relation to measurement-based quantum computing in a twisted spacetime. We also propose a generalization to more general stabilizer codes, and we present computer analysis of optimal rotations in low dimensions. We present methods to do logical Clifford operations on these codes using crystalline symmetries and surgery, and we present a method for state injection at low noise into stabilizer quantum codes generalizing previous ideas for the two-dimensional toric code.

Metal-oxide-semiconductor (MOS) technology is a promising platform for developing quantum computers based on spin qubits. Scaling this approach will benefit from compact and sensitive sensors that minimize constraints on qubit connectivity while being industrially manufacturable. Here, we demonstrate a compact dispersive spin-qubit sensor, a single-electron box (SEB), within a bilinear unit cell of planar MOS quantum dots (QDs) fabricated using an industrial grade 300 mm wafer process. By independent gate control of the SEB and double-quantum-dot tunnel rates, we optimize the sensor to achieve a readout fidelity of 99.92% in 340us (99% in 20us), fidelity values on a par with the best obtained with less compact sensors. Furthermore, we develop a Hidden Markov Model of the two-electron spin dynamics that enables a more accurate calculation of the measurement outcome and hence readout fidelity. Our results show how high-fidelity sensors can be introduced within silicon spin-qubit architectures while maintaining sufficient qubit connectivity as well as providing faster readout and more efficient initialisation schemes.

The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in simulating classical dynamics with long-range interactions. However, many real-world classical systems, such as those arising from partial differential equations, exhibit only local interactions. The question remains whether quantum algorithms can still provide exponential speedup under this condition. In this work, we thoroughly characterize the computational complexity of quantum algorithms for simulating such geometrically local systems. First, we dequantize the quantum algorithm for simulating short-time (polynomial-time) dynamics of such systems. This implies that the problem of simulating this dynamics does not yield any exponential quantum advantage. Second, we show that quantum algorithms for short-time dynamics have the same computational complexity as polynomial-time probabilistic classical computation. Third, we show that the computational complexity of quantum algorithms for long-time (exponential-time) dynamics is captured by exponential-time and polynomial-space quantum computation. This suggests a super-polynomial time advantage when restricting the computation to polynomial-space, or an exponential space advantage otherwise. This work offers new insights into the complexity of classical dynamics governed by partial differential equations, providing a pathway for achieving quantum advantage in practical problems.

Simple few-body systems often serve as theoretical laboratories across various branches of theoretical physics. A prominent example is the two-electron Harmonium model, which has been widely studied over the past three decades to gain insights into the nature of the electron-electron correlations in many-electron quantum systems. Building on our previous work [Phys. Rev. B 108, 245155 (2023)], we introduce an analogous model consisting of an electron and a positively charged particle (PCP) with variable mass, interacting via Coulomb forces while confined by external harmonic potentials. Termed the exotic Harmonium model, this provides insights into the electron-PCP correlations, a cornerstone of the emerging field of the ab initio study of multi-component many-body quantum systems. Through a systematic exploration of the parameter space and numerical solutions of the corresponding Schr\"odinger equation, we identify two extreme regimes: the atom-like and the particle-in-trap-like behavior. The electron-PCP correlation dominates in the atom-like regime, significantly influencing physical observables, while its role diminishes in the particle-in-trap-like limit. Between these two extremes lies a complex intermediate regime that challenges qualitative interpretation. Overall, the exotic Harmonium model offers a powerful framework to unravel the electron-PCP correlations across diverse systems, spanning particles of varying masses and conditions, from ambient to high-pressure environments.

Quantum state tomography (QST) is an essential technique for reconstructing the density matrix of an unknown quantum state from measurement data, crucial for quantum information processing. However, conventional QST requires an exponentially growing number of measurements as the system dimension increases, posing a significant challenge for high-dimensional systems. To mitigate this issue, compressed sensing quantum state tomography (CS-QST) has been proposed, significantly reducing the required number of measurements. In this study, we investigate the impact of basis selection in CS-QST for qudit systems, which are fundamental to high-dimensional quantum information processing. Specifically, we compare the efficiency of the generalized Gell-Mann (GGM) and Heisenberg-Weyl observable (HWO) bases by numerically reconstructing density matrices and evaluating reconstruction accuracy using fidelity and trace distance metrics. Our results demonstrate that, while both bases allow for successful density matrix reconstruction, the HWO basis becomes more efficient as the qudit dimension increases. Furthermore, we find the best fitting curves that estimate the number of measurement operators required to achieve a fidelity of at least 95%. These findings highlight the significance of basis selection in CS-QST and provide valuable insights for optimizing measurement strategies in high-dimensional quantum state tomography.

Entanglement is a defining feature of many-body quantum systems and is an essential requirement for quantum computing. It is therefore useful to study physical processes which generate entanglement within a large system, as they maybe replicated for applications involving the said requirements in quantum information processing. A possible avenue to maximize entanglement generation is to rely on the phenomena of information scrambling, i.e. transport of initially localized information throughout the system. Here the rationale is that the spread of information carries with it an inherent capacity of entanglement generation. Scrambling greatly depends upon the dynamical nature of the system Hamiltonian, and the interplay between entanglement generation and information scrambling maybe investigated taking a chain of interacting spins on a one dimensional lattice. This system is analogous to an array of qubits and this relative simplicity implies that the resulting unitary dynamics can be efficiently simulated using present-day cloud based NISQ devices. In our present work, we consider such a spin model which is made up of nearest and next nearest neighbor XXZ Model, along with an introduced coupling term lambda. This coupling term serves as a tuning parameter which modifies the dynamical nature of the system from the integrable to the quantum chaotic regime. In order to quantify the entanglement generated within the system we use the more general multipartite metric which computes the average entanglement across all system bipartitions to obtain a global picture of the entanglement structure within the entire system.

The Gottesman-Kitaev-Preskill (GKP) codes are known to achieve optimal rates under displacement noise and pure loss channels, which establishes theoretical foundations for its optimality. However, such optimal rates are only known to be achieved at a discrete set of noise strength with the current self-dual symplectic lattice construction. In this work, we develop a new coding strategy using concatenated continuous variable - discrete variable encodings to go beyond past results and establish GKP's optimal rate over all noise strengths. In particular, for displacement noise, the rate is obtained through a constructive approach by concatenating GKP codes with a quantum polar code and analog decoding. For pure loss channel, we prove the existence of capacity-achieving GKP codes through a random coding approach. These results highlight the capability of concatenation-based GKP codes and provides new methods for constructing good GKP lattices.

As quantum computing progresses towards the early fault-tolerant regime, quantum error correction will play a crucial role in protecting qubits and enabling logical Clifford operations. However, the number of logical qubits will initially remain limited, posing challenges for resource-intensive tasks like magic state distillation. It is therefore essential to develop efficient methods for implementing non-Clifford operations, such as small-angle rotations, to maximise the computational capabilities of devices within these constraints. In this work, we introduce mitigated magic dilution (MMD) as an approach to synthesise small-angle rotations by employing quantum error mitigation techniques to sample logical Clifford circuits given noisy encoded magic states. We explore the utility of our approach for the simulation of the 2D Fermi-Hubbard model. We identify evolution time regimes where MMD outperforms the Ross-Selinger gate synthesis method [Quantum Inf.\ Comp.\ \textbf{16}, 901-953 (2016), arXiv:1403.2975] in the number of noisy encoded magic states required for square lattices up to size $8 \times 8$. Moreover, we demonstrate that our method can provide a practical advantage which is quantified by a better-than-quadratic improvement in the resource requirements for small-angle rotations over classical simulators. This work paves the way for early fault-tolerant demonstrations on devices supporting millions of quantum operations, the so-called MegaQuOp regime.

Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally obtained solutions and compare them to numerically exact calculations in quantum critical systems. We demonstrate that interpreting the cost functional as an integral permits the deployment of iterative quadrature schemes, thereby reducing the required number of measurements by several orders of magnitude. We further show that a modified ansatz captures deviations from the Bisognano-Wichmann form in lattice models, improves convergence, and provides a cost-function-level diagnostic for quantum phase transitions. Finally, we establish that a low cost value does not by itself guarantee convergence in trace distance. Nevertheless, it faithfully reproduces degeneracies and spectral gaps, which are essential for applications to topological phases.

Sampling from high-dimensional and structured probability distributions is a fundamental challenge in computational physics, particularly in the context of lattice field theory (LFT), where generating field configurations efficiently is critical, yet computationally intensive. In this work, we apply a previously developed hybrid quantum-classical normalizing flow model to explore quantum-enhanced sampling in such regimes. Our approach embeds parameterized quantum circuits within a classical normalizing flow architecture, leveraging amplitude encoding and quantum entanglement to enhance expressivity in the generative process. The quantum circuit serves as a trainable transformation within the flow, while classical networks provide adaptive coupling and compensate for quantum hardware imperfections. This design enables efficient density estimation and sample generation, potentially reducing the resources required compared to purely classical methods. While LFT provides a representative and physically meaningful application for benchmarking, our focus is on improving the sampling efficiency of generative models through quantum components. This work contributes toward the development of quantum-enhanced generative modeling frameworks that address the sampling bottlenecks encountered in physics and beyond.

Modern physics proposals present deep tensions between seemingly contradictory descriptions of reality. Views of wave-particle duality, black hole complementarity, and the Unruh effect demand explanations that shift depending on how a system is observed. However, traditional models of scientific explanation impose a fixed structure that fails to account for varying observational contexts. This paper introduces context-dependent mapping, a framework that reorganizes physical laws into self-consistent subsets structured around what can actually be observed in a given context. By doing so, it provides a principled way to integrate complementarity into the philosophy of explanation.

The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field, and has later been generalized to Chern insulators without net magnetization. Here, further extending the realm of the quantum Hall effect, we report on the robust occurrence of an integer quantized transverse conductance at the onset of disorder in a microscopic lattice model all bands of which are topologically trivial (zero Chern number). We attribute this remarkable phenomenon to the energetic separation of substantial but non-quantized Berry fluxes within the topologically trivial bands. Adding a random disorder potential then nudges the system into a stable quantum Hall phase from an extended critical regime of the clean system obtained by placing the Fermi energy within a broad window in either of the trivial bands. Our results are corroborated by extensive numerical transport simulations as well as the analysis of several complementary topological markers.

Femtosecond laser-writing offers distinct capabilities for fabrication, including three-dimensional, multi-material, and sub-diffraction-limited patterning. In particular, demonstrations of laser-written quantum emitters and photonic devices with superior optical properties have attracted attention. Recently, gallium nitride (GaN) has been reported to host quantum emitters with narrow and bright zero-phonon photoluminescence from ultraviolet to telecom ranges. However, emitters formed during epitaxy are randomly positioned, and until now, it has not been possible to fabricate quantum emitters in ordered arrays. In this paper, we employ femtosecond laser writing to create nano-ablations with sub-diffraction-limited diameter, and use rapid thermal annealing to activate co-located stable emitters. The emitters show MHz antibunched emission with a sharp spectral peak at room temperature. Our study not only presents an efficient approach to laser-written nanofabrication on GaN but also offers a promising pathway for the deterministic creation of quantum emitters in GaN, shedding light on the underlying mechanisms involved.

This work introduces the High-Order Hermite Optimization (HOHO) method, an open-loop discrete adjoint method for quantum optimal control. Our method is the first of its kind to efficiently compute exact (discrete) gradients when using continuous, parameterized control pulses while solving the forward equations (e.g. Schrodinger's equation or the Linblad master equation) with an arbitrarily high-order Hermite Runge-Kutta method. The HOHO method is implemented in QuantumGateDesign.jl, an open-source software package for the Julia programming language, which we use to perform numerical experiments comparing the method to Juqbox.jl. For realistic model problems we observe speedups up to 775x.

We analyze the matching of high and low temperature expansions of the effective action of massive scalar fields confined between two infinite walls with different boundary conditions. One remarkable low temperature effect is the exponential decay of the vacuum energy with the separation of the walls and the fact that the rate of decay is half for the boundary conditions which involve a connection between the boundary conditions of the two walls. In particular, the rate for Dirichlet boundary conditions is double than that of periodic boundary conditions.

The next generation of technology is rooted in quantum-based advancements. The entangled photon pair sources play a pivotal role in a wide range of advanced quantum applications, including quantum high precision sensors, communication, computing, cryptography and so on. Scalable on-chip quantum photonic devices have the potential to drive game changing developments in this field. This review article highlights recent breakthroughs in the generation of entangled photon pairs in two dimensional (2D) van der Waals (vdW) materials, with a focus on their applicability to quantum technologies and plausible on-chip integration technology. The article begins by discussing the fundamental principles of entangled photon pairs generation. It provides a comprehensive review of the origin and generation of entangled photons in emerging vdW materials, alongside various optical quantum characterization techniques. The review then explores key physical parameters of the quantum states associated with entangled photon pairs. Additionally, it examines concepts related to the realization of paired photon generation at the quantum limit. The final section focuses on the potential for on-chip integrated quantum device applications. Beyond highlighting recent advancements in quantum-based research, the review also outlines current limitations and future prospects aimed at advancing the field

Quantum-classical Hybrid Machine Learning (QHML) models are recognized for their robust performance and high generalization ability even for relatively small datasets. These qualities offer unique advantages for anti-cancer drug response prediction, where the number of available samples is typically small. However, such hybrid models appear to be very sensitive to the data encoding used at the interface of a neural network and a quantum circuit, with suboptimal choices leading to stability issues. To address this problem, we propose a novel strategy that uses a normalization function based on a moderated gradient version of the $\tanh$. This method transforms the outputs of the neural networks without concentrating them at the extreme value ranges. Our idea was evaluated on a dataset of gene expression and drug response measurements for various cancer cell lines, where we compared the prediction performance of a classical deep learning model and several QHML models. These results confirmed that QHML performed better than the classical models when data was optimally normalized. This study opens up new possibilities for biomedical data analysis using quantum computers.

Atomic diffraction through a nanograting is a powerful tool to probe the Casimir-Polder potential. Achieving precise measurements require simulations to bridge theory and experiment. In this context, we present various approximations and methods of Casimir-Polder potentials, and we analyze their impact on matter-wave diffraction patterns. Our analysis includes the pairwise summation approach, the proximity force approximation, and multiple scattering expansion method. Furthermore, we demonstrate that the influence of Casimir-Polder interactions extends up to 25 nm before and after the nanograting slit, highlighting the importance of accounting for this effect in any accurate analysis.

Integration of electron spin resonance (ESR) in a scanning tunneling microscope (STM) has enabled an all-electrical control of atomic and molecular spins on solid surfaces with atomic-scale precision and energy resolution beyond thermal limitations. Further, coherent manipulation and detection of individual spins in an ESR-STM establishes a powerful quantum platform, allowing for the implementation of fundamental quantum logic operations to on-surface identical qubits. In this review, we introduce recent advances of ESR-STM, focusing on its application to atomic-scale qubits and extension to molecular qubit systems. We discuss the principles underlying ESR-STM, followed by single-spin addressability, coherent control via Rabi oscillations, and quantum state readout through frequency-resolved detection. We further demonstrate multi-qubit control architectures enabled by atom manipulation and local magnetic field engineering, culminating in the realization of multi-qubit logic gates such as the Controlled-NOT and Toffoli gates. These implementations highlight the specialty of ESR-STM towards atomic-scale quantum circuits. Indeed, ESR-STM can be an excellent tool to perform and evaluate quantum operations in molecular qubits. The results reviewed in this collection establish ESR-STM as a versatile tool for advancing quantum coherent science at the atomic and molecular level in solid-state environments.

Optical tweezers are a powerful tool for the precise positioning of a variety of small objects, including single neutral atoms. Once trapped, atoms can be cooled to the motional ground state of the tweezers. For a more advanced control of their spatial wavefunction, we report here a simple method to squeeze their motion, and the protocol to measure the squeezing factor based on momentum spreading estimation. We explore the limitations set by the technical imperfections of the tweezers, as well as the more fundamental limit set by their anharmonicity, and finally demonstrate a squeezing of 5.8 dB. The implementation of motional squeezing allows to push back the limit set by the position quantum noise and thus to explore more extreme situations requiring atoms positioned with nanometric precision.

Embedding materials in optical cavities has emerged as a strategy for tuning material properties. Accurate simulations of electrons in materials interacting with quantum photon fluctuations of a cavity are crucial for understanding and predicting cavity-induced phenomena. In this article, we develop a non-perturbative quantum electrodynamical approach based on a photon-free self-consistent Hartree-Fock framework to model the coupling between electrons and cavity photons in crystalline materials. We apply this theoretical approach to investigate graphene coupled to the vacuum field fluctuations of cavity photon modes with different types of polarizations. The cavity photons introduce nonlocal electron-electron interactions, originating from the quantum nature of light, that lead to significant renormalization of the Dirac bands. In contrast to the case of graphene coupled to a classical circularly polarized light field, where a topological Dirac gap emerges, the nonlocal interactions induced by a quantum linearly polarized photon mode give rise to the formation of flat bands and the opening of a topologically trivial Dirac gap. When two symmetric cavity photon modes are introduced, Dirac cones remain gapless, but a Fermi velocity renormalization yet indicates the relevant role of nonlocal interactions. These effects disappear in the classical limit for coherent photon modes. This new self-consistent theoretical framework paves the way for the simulation of non-perturbative quantum effects in strongly coupled light-matter systems, and allows for a more comprehensive discovery of novel cavity-induced quantum phenomena.

The emergence of hybrid quantum-classical machine learning (HQML) models opens new horizons of computational intelligence but their fundamental complexity frequently leads to black box behavior that undermines transparency and reliability in their application. Although XAI for quantum systems still in its infancy, a major research gap is evident in robust global and local explainability approaches that are designed for HQML architectures that employ quantized feature encoding followed by classical learning. The gap is the focus of this work, which introduces QuXAI, an framework based upon Q-MEDLEY, an explainer for explaining feature importance in these hybrid systems. Our model entails the creation of HQML models incorporating quantum feature maps, the use of Q-MEDLEY, which combines feature based inferences, preserving the quantum transformation stage and visualizing the resulting attributions. Our result shows that Q-MEDLEY delineates influential classical aspects in HQML models, as well as separates their noise, and competes well against established XAI techniques in classical validation settings. Ablation studies more significantly expose the virtues of the composite structure used in Q-MEDLEY. The implications of this work are critically important, as it provides a route to improve the interpretability and reliability of HQML models, thus promoting greater confidence and being able to engage in safer and more responsible use of quantum-enhanced AI technology.

We predict the existence of two tri-critical quantum Lifshitz points in recently discovered $d$-wave altermagnetic metals subjected to an external magnetic field. These points connect a spatially modulated Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase, a uniform polarized Bardeen--Cooper--Schrieffer (BCS) superconducting phase, and the normal metallic phase in a nontrivial manner. Depending on whether the FFLO state is primarily induced by the magnetic field or by $d$-wave altermagnetism, we classify the corresponding Lifshitz points as field-driven or altermagnetism-driven, respectively. Notably, the two types exhibit distinct behaviors: the transition from the FFLO phase to the polarized BCS phase is first-order near the field-driven Lifshitz point, as might be expected, whereas it becomes continuous near the altermagnetism-driven Lifshitz point. We further explore the effects of finite temperature and find that the altermagnetism-driven Lifshitz point is significantly more sensitive to thermal fluctuations.

The non-Hermitian skin effect, nonreciprocity-induced anomalous localization of an extensive number of eigenstates, represents a hallmark of non-Hermitian topological systems with no analogs in Hermitian systems. Despite its significance across various open classical and quantum systems, the influence of nonlinearity has remained largely unclear. Here, we reveal the Hopf bifurcation of the nonlinear skin effect as a critical phenomenon unique to nonlinear non-Hermitian systems. We demonstrate that nonlinearity destabilizes skin states and instead gives rise to the emergence of delocalized states associated with limit cycles in phase space. We also uncover the algebraically localized critical skin effect precisely at the Hopf bifurcation point. We illustrate these behavior in a nonlinear extension of the Hatano-Nelson model in both continuum and lattice. Our work shows a significant role of nonlinearity in the skin effect and uncovers rich phenomena arising from the interplay between non-Hermiticity and nonlinearity.

Spectroscopic data on alkali-atom dimers residing on the surface of liquid helium nanodroplets have revealed that they are detected primarily in the weakly bound, metastable, spin-triplet state. Here, by measuring the magnetic Stern-Gerlach deflection of a sodium-doped nanodroplet beam, we transparently demonstrate the abundance of high-magnetic-moment dimers. Their electron spins thermalize with the cryogenic superfluid droplets and become fully oriented by the external magnetic field.

We uncover a new class of dynamical quantum instability in driven magnets leading to emergent enhancement of antiferromagnetic correlations even for purely ferromagnetic microscopic couplings. A primary parametric amplification creates a frequency-tuned nested magnon distribution in momentum space, which seeds a secondary instability marked by the emergence of enhanced antiferromagnetic correlations, mirroring Fermi surface nesting instabilities in electronic systems. In sharp contrast to the fermionic case, however, the magnon-driven instability is intrinsically non-equilibrium and fundamentally inaccessible in thermal physics. Its quantum mechanical origin sets it apart from classical instabilities such as Faraday and modulation instabilities, which underlie several instances of dynamical behavior observed in magnetic and cold-atom systems.

We demonstrate background-free imaging and sideband cooling of a single 133Cs atom via the narrow-line 6S1/2 to 5D5/2 electric quadrupole transition in a 1064 nm optical tweezer. The 5D5/2 state decays through the 6P3/2 state to the ground state, emitting an 852 nm wavelength photon that allows for background-free imaging. By encoding both spin and orbital angular momentum onto the 685 nm excitation light, we achieve background-free fluorescence histograms with 99.58(3)% fidelity by positioning the atom at the dark center of a vortex beam. Tuning the tweezer polarization ellipticity realizes a magic trap for the stretched F = 4, mF = 4 to F' = 6, mF' = 6 cycling transition. We cool to 5 uK in a 1.1 mK trap and outline a strategy for ground-state cooling. We compare cooling performance across different sideband regimes, while also exploring how the orbital angular momentum of structured light controls the selection rules for quadrupole transitions. These results expand the toolbox for high-fidelity quantum control and cooling in alkali-atom tweezer arrays.

Bethe strings are bound states of constituent particles in a variety of interacting many-body one-dimensional (1D) integrable quantum models relevant to magnetism, nanophysics, cold atoms and beyond. As emergent fundamental excitations, they are predicted to collectively reshape observable equilibrium and dynamical properties. Small individual Bethe strings have recently been observed in quantum magnets and superconducting qubits. However, creating states featuring intermixtures of many, including large, strings remains an outstanding experimental challenge. Here, using nearly integrable ultracold Bose gases, we realize such intermixtures of Bethe strings out of equilibrium, by dynamically tuning interactions from repulsive to attractive. We measure the average binding energy of the strings, revealing the presence of bound states of more than six particles. We find further evidence for them in the momentum distribution and in Tan's contact, connected to the correlated density. Our data quantitatively agree with predictions from generalized hydrodynamics (GHD). Manipulating intermixtures of Bethe strings opens new avenues for understanding quantum coherence, nonlinear dynamics and thermalization in strongly-interacting 1D systems.