The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a compressed, lower-information representation of quantum reality. Quantum mechanics encodes significantly more information through superposition, entanglement, and phase coherence, which are lost due to decoherence, phase averaging, and measurement, reducing the system to a classical probability distribution. This transition is quantified using Kolmogorov complexity, where classical systems require \( O(N) \) bits of information, while quantum descriptions require \( O(2^N) \), showing an exponential reduction in complexity. Further justification comes from Ehrenfest's theorem, which ensures that quantum expectation values obey Newton's laws, and path integral suppression, which eliminates non-classical trajectories when \( S \gg \hbar \). Thus, rather than viewing quantum mechanics as an extension of classical mechanics, we argue that classical mechanics is a lossy, computationally reduced encoding of quantum physics, emerging from a systematic loss of quantum correlations.

To transport high-quality quantum state between two distant qubits through one-dimensional spin chains, the perfect state transfer (PST) method serves as the first choice, due to its natively perfect transfer fidelity that is independent of the system dimension. However, the PST requires a precise modulation of the local pulse parameters as well as an accurate timing of dynamic evolution, and is thus very sensitive to variations in practice. Here, we propose a protocol for achieving quantum-preserved transport of excitations using an array of Rydberg-dressed atoms, enabled by optimal control of minimally global parameters. By treating the weak coupling of two marginal array atoms as a perturbation, an effective spin-exchange model with highly tunable interactions between the external weak and the inner strong driving atoms can be established, which allows for coherent excitation transfer even with large atomic position fluctuation. We furthermore show that the existence of long-time excitation propagation unattainable for systems under antiblockade facilitation conditions. Our results highlight an easily-implemented scheme for studying the dynamics of spin systems using Rydberg atoms and may guide the avenue to the engineering of complex many-body dynamics.

Pilot wave theory endows particles with definite positions at all times governed by deterministic dynamics. However, individual particle trajectories are generically undetectable by experiment. This idea might seem to be contested in light of two proposals: (1) So-called 'weak velocity measurements', allegedly detecting Bohmian trajectories by weakly probing a quantum system without essentially disturbing it, and (2) the so-called 'surrealistic' trajectories experiment which supposedly establishes a conflict between the 'actual' position of a particle and its position derived from pilot wave theory. Although both attempts shed light on the nature of Bohmian particles, neither constitute empirical or theoretical evidence in favour or against pilot wave theory. Both instances admit a straightforward standard quantum mechanical interpretation compatible with the predictions of Bohmian theories. It is concluded that the puzzles arise from the absence of a coherent account of what quantum mechanical measurements signify.

We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random sampling and approximate counting and employs QAOA as a solution sampler. We first prove that VQCount improves upon previous work by reducing exponentially the number of samples needed to obtain an approximation within a multiplicative factor of the exact count. Using tensor network simulations, we then study the typical performance of VQCount with shallow circuits on synthetic instances of two #P-hard problems, positive #NAE3SAT and positive #1-in-3SAT. We employ the original quantum approximate optimization algorithm version of QAOA, as well as the Grover-mixer variant which guarantees a uniform solution probability distribution. We observe a tradeoff between QAOA success probability and sampling uniformity, which we exploit to achieve an exponential gain in efficiency over naive rejection sampling. Our results highlight the potential and limitations of variational algorithms for approximate counting.

Eigenstate thermalization has played a prominent role as a determiner of the validity of quantum statistical mechanics since von Neumann's early works on quantum ergodicity. However, its connection to the dynamical process of quantum thermalization relies sensitively on nondegeneracy properties of the energy spectrum, as well as detailed features of individual eigenstates that are effective only over correspondingly large timescales, rendering it generically inaccessible given practical timescales and finite experimental resources. Here, we introduce the notion of energy-band thermalization to address these limitations, which coarse-grains over energy level spacings with a finite energy resolution. We show that energy-band thermalization implies the thermalization of an observable in almost all physical states over accessible timescales without relying on microscopic properties of the energy eigenvalues or eigenstates, and conversely, can be efficiently accessed in experiments via the dynamics of a single initial state (for a given observable) with only polynomially many resources in the system size. This allows us to directly determine thermalization, including in the presence of conserved charges, from this state: Most strikingly, if an observable thermalizes in this initial state over a finite range of times, then it must thermalize in almost all physical initial states over all longer timescales. As applications, we derive a finite-time Mazur-Suzuki inequality for quantum transport with approximately conserved charges, and establish the thermalization of local observables over finite timescales in almost all accessible states in (generally inhomogeneous) dual-unitary quantum circuits. We also propose measurement protocols for general many-qubit systems. This work initiates a rigorous treatment of quantum thermalization in terms of experimentally accessible quantities.

The birth, life, and death of Maxwell's demon provoked a profound discussion about the interplay between thermodynamics, computation, and information. Even after its exorcism, the demon continues to inspire a multidisciplinary field. This tutorial offers a comprehensive overview of Maxwell's demon and its enduring influence, bridging classical concepts with modern insights in thermodynamics, information theory, and quantum mechanics.

Over the past two decades, the overlap matrix approach has been developed to compute quantum entanglement in free-fermion systems, particularly to calculate entanglement entropy and entanglement negativity. This method involves the use of partial trace and partial transpose operations within the overlap matrix framework. However, previous studies have only considered the conventional partial transpose in fermionic systems, which does not account for fermionic anticommutation relations. Although the concept of a fermionic partial transpose was introduced in \cite{Shapourian2017prb}, it has not yet been systematically incorporated into the overlap matrix framework. In this paper, we introduce the fermionic partial transpose into the overlap matrix approach, provide a systematic analysis of the validity of partial trace and partial transpose operations, and derive an explicit formula for calculating entanglement negativity in bipartite systems. Additionally, we numerically compute the logarithmic negativity of two lattice models to verify the Gioev-Klich-Widom scaling law. For tripartite geometries, we uncover limitations of the overlap matrix method and demonstrate that the previously reported logarithmic negativity result for a homogeneous one-dimensional chain in a disjoint interval geometry exceeds its theoretical upper bound. Our findings contribute to a deeper understanding of partial trace and partial transpose operations in different representations.

Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL) - the fundamental precision bound set by quantum mechanics - is often hindered by noise-induced decoherence, which typically reduces achievable precision to the standard quantum limit (SQL). While quantum error correction (QEC) can recover the HL under Markovian noise, its applicability to non-Markovian noise remains less explored. In this work, we analyze a hidden Markov model in which a quantum probe, coupled to an inaccessible environment, undergoes joint evolution described by Lindbladian dynamics, with the inaccessible degrees of freedom serving as a memory. We derive generalized Knill-Laflamme conditions for the hidden Markov model and establish three types of sufficient conditions for achieving the HL under non-Markovian noise using QEC. Additionally, we demonstrate the attainability of the SQL when these sufficient conditions are violated, by analytical solutions for special cases and numerical methods for general scenarios. Our results not only extend prior QEC frameworks for metrology but also provide new insights into precision limits under realistic noise conditions.

The graph isomorphism problem remains a fundamental challenge in computer science, driving the search for efficient decision algorithms. Due to its ambiguous computational complexity, heuristic approaches such as simulated annealing are frequently used to explore the solution space selectively. These methods often achieve high probabilities of identifying solutions quickly, avoiding the exhaustive enumeration required by exact algorithms. However, traditional simulated annealing usually struggles with low sampling efficiency and reduced solution-finding probability in complex or large graph problems. In this study, we integrate the principles of quantum technology to address the graph isomorphism problem. By mapping the solution space to a quantum many-body system, we developed a parameterized model for variational simulated annealing. This approach emphasizes the regions of the solution space that are most likely to contain the optimal solution, thereby enhancing the search accuracy. Artificial neural networks were utilized to parameterize the quantum many-body system, leveraging their capacity for efficient function approximation to perform accurate sampling in the intricate energy landscapes of large graph problems.

We determine the Kirkwood-Dirac quasiprobability (KDQ) distribution associated to the stochastic instances of internal energy variations for the quantum system and environment particles in coherent Markovian collision models. In the case the interactions between the quantum system and the particles do not conserve energy, the KDQ of the non-energy-preserving stochastic work is also derived. These KDQ distributions can account for non-commutativity, and return the unperturbed average values and variances for a generic interaction-time, and generic local initial states of the quantum system and environment particles. Using this nonequilibrium-physics approach, we certify the conditions under which the collision process of the model exhibits quantum traits, and we quantify the rate of energy exchanged by the quantum system by looking at the variance of the KDQ energy distributions. Finally, we propose an experimental test of our results on a superconducting quantum circuit implementing a qubit system, with microwave photons representing the environment particles.

We show that the Cauchy-Schwarz inequality provides a simple yet general bound that limits the accuracy of light-matter theories which retain only finite numbers of material energy levels. A corollary is that unitary rotations within a truncated space cannot transform between gauges, because the contrary assumption yields incorrect predictions. In particular, a widespread model obtained using such a rotation and treated as a Coulomb gauge model within a substantial body of literature, yields incorrect predictions under this assumption. The simplest system of a single dipole coupled to a single photonic mode in one spatial dimension is analysed in detail.

In this study, we investigate the optical absorption within the conduction-subbands of a cylindrical GaN/AlN quantum wire. We analyze the optical absorption rate and the real part of the dielectric function for both quantum wire (QWR) and quantum dot (QD) structures in the presence of donor-impurity states. The results cover that the density of states associated with free motion in the QWR structure leads to a lower optical absorption compared to the QDs, as evidenced by the optical spectra. This study advances the understanding of GaN/AlN heterostructures by offering a comprehensive analysis of the optical properties of QWRs and QDs, especially under donor-doping situation. As a result, the outcomes provide a clear evidence of the effect of semiconductor nanostructures on the optical properties of optoelectronic devices.

The measurement of tunneling times in strong-field ionization has been the topic of much controversy in recent years, with the attoclock and Larmor clock being two of the main contenders for correctly reproducing these times. By expressing the attoclock as the weak value of temporal delay, we extend its meaning beyond the traditional setup. This allows us to calculate the attoclock time for a static one-dimensional tunneling model consisting of a binding delta potential and a constant electric field. We apply the Steinberg weak-value interpretation of the Larmor clock. Using this definition, we obtain the position-resolved time density during tunnel ionization, yielding a non-zero Larmor tunneling time. Our model allows us to derive the analogue of the position-resolved attoclock tunneling time. While non-zero at the tunnel exit, it vanishes at the detector, far away from the atom. Formally, this means that the attoclock does not measure the "local" Larmor time, but instead a "non-local" time closely related to the phase time.

A lattice beam configuration which results in an isotropic 3D trap near the surface of an atom chip is described. The lattice is formed near the surface of a reflectively coated atom chip, where three incident beams and three reflected beams intersect. The coherent interference of these six beams form a phase-stable optical lattice which extends to the surface of the atom chip. The lattice is experimentally realized and the trap frequency is measured. Degenerate Raman sideband cooling is performed in the optical lattice, cooling 80 million atoms to 1.1 $\mu$K.

Multi-objective combinatorial optimization in wireless communication networks is a challenging task, particularly for large-scale and diverse topologies. Recent advances in quantum computing offer promising solutions for such problems. Coherent Ising Machines (CIM), a quantum-inspired algorithm, leverages the quantum properties of coherent light, enabling faster convergence to the ground state. This paper applies CIM to multi-objective routing optimization in wireless multi-hop networks. We formulate the routing problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem and map it onto an Ising model, allowing CIM to solve it. CIM demonstrates strong scalability across diverse network topologies without requiring topology-specific adjustments, overcoming the limitations of traditional quantum algorithms like Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). Our results show that CIM provides feasible and near-optimal solutions for networks containing hundreds of nodes and thousands of edges. Additionally, a complexity analysis highlights CIM's increasing efficiency as network size grows

In this paper, we propose a novel framework for efficiently and accurately estimating Lipschitz constants in hybrid quantum-classical decision models. Our approach integrates classical neural network with quantum variational circuits to address critical issues in learning theory such as fairness verification, robust training, and generalization. By a unified convex optimization formulation, we extend existing classical methods to capture the interplay between classical and quantum layers. This integrated strategy not only provide a tight bound on the Lipschitz constant but also improves computational efficiency with respect to the previous methods.

The reconstruction of density matrices from measurement data (quantum state tomography) is the most comprehensive method for assessing the accuracy and performance of quantum devices. Existing methods to reconstruct two-photon density matrices require the detection of both photons unless a priori information is available. Based on the concept of quantum-induced coherence by path identity, we present an approach to quantum state tomography that circumvents the requirement of detecting both photons. We show that an arbitrary two-qubit density matrix, which can contain up to fifteen free parameters, can be fully reconstructed from single-photon measurement data without any postselection and a priori information. In addition to advancing an alternative approach to quantum state measurement problems, our results also have notable practical implications. A practical challenge in quantum state measurement arises from the fact that effective single-photon detectors are not readily accessible for a wide spectral range. Our method, which eliminates the need for coincidence measurements, enables quantum state tomography in the case where one of the two photons is challenging or impossible to detect. It therefore opens the door to measuring quantum states hitherto inaccessible.

The Dirac equation, central to relativistic quantum mechanics, governs spin-$\frac{1}{2}$ particles and their antiparticles, with each spinor component satisfying the Klein-Gordon equation - the quantum counterpart of the relativistic mass shell condition. Our prior work [V. Yordanov, Sci. Rep. 14, 6507 (2024)] derived Dirac equation using stochastic optimal control (SOC) theory by linearizing the Lagrangian's kinetic term and the Hamilton-Jacobi-Bellman equation, but failed to preserve the mass shell condition. Here, we introduce a novel SOC derivation that retains the nonlinear kinetic term and integrates spin-electromagnetic coupling into the potential, ensuring relativistic consistency. This approach not only addresses the limitations of the previous model but also deepens the link between stochastic mechanics and quantum theory, offering fresh insights into relativistic quantum phenomena.

Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding probabilities have been investigated and some interesting things have been analytically discovered. They are, for instance, ballistic behavior, localization, or a gap. We study a 1-dimensional quantum walk in this paper. Although the walker launches off a location under a localized initial state, some numerical experiments show that the quantum walker does not seem to distribute around the launching location, which suggests that the probability distribution holds a gap around the launching location. To prove the gap analytically, we derive a long-time limit distribution, from which one can tell more details about the finding probability.

Quantum squeezed states, with reduced quantum noise, have been widely utilized in quantum sensing and quantum error correction applications. However, generating and manipulating these nonclassical states with a large squeezing degree typically requires strong nonlinearity, which inevitably induces additional decoherence that diminishes the overall performance. Here, we demonstrate the generation and amplification of squeezed states in a superconducting microwave cavity with weak Kerr nonlinearity. By subtly engineering an off-resonant microwave drive, we observe cyclic dynamics of the quantum squeezing evolution for various Fock states |N> with N up to 6 in displaced frame of the cavity. Furthermore, we deterministically realize quantum squeezing amplification by alternately displacing the Kerr oscillator using the Trotterization technique, achieving a maximum squeezing degree of 14.6 dB and squeezing rate of 0.28 MHz. Our hardware-efficient displacement-enhanced squeezing operations provide an alternative pathway for generating large squeezed states, promising potential applications in quantum-enhanced sensing and quantum information processing.

In this paper, we design and experimentally implement various robust quantum unitary transformations (gates) acting on $d$-dimensional vectors (qudits) by tuning a single control parameter using optimal control theory. The quantum state is represented by the momentum components of a Bose-Einstein condensate (BEC) placed in an optical lattice, with the lattice position varying over a fixed duration serving as the control parameter. To evaluate the quality of these transformations, we employ standard quantum process tomography. In addition, we show how controlled unitary transformations can be used to extend state stabilization to global stabilization within a controlled vector subspace. Finally, we apply them to state tomography, showing how the information about the relative phase between distant momentum components can be extracted by inducing an interference process.

Multiparameter quantum estimation theory plays a crucial role in advancing quantum metrology. Recent studies focused on fundamental challenges such as enhancing precision in the presence of incompatibility or sloppiness, yet the relationship between these features remains poorly understood. In this work, we explore the connection between sloppiness and incompatibility by introducing an adjustable scrambling operation for parameter encoding. Using a minimal yet versatile two-parameter qubit model, we examine the trade-off between sloppiness and incompatibility and discuss: (1) how information scrambling can improve estimation, and (2) how the correlations between the parameters and the incompatibility between the symmetric logarithmic derivatives impose constraints on the ultimate quantum limits to precision. Through analytical optimization, we identify strategies to mitigate these constraints and enhance estimation efficiency. We also compare the performance of joint parameter estimation to strategies involving successive separate estimation steps, demonstrating that the ultimate precision can be achieved when sloppiness is minimized. Our results provide a unified perspective on the trade-offs inherent to multiparameter qubit statistical models, offering practical insights for optimizing experimental designs.

Single-qubit gates are in many quantum platforms applied using a linear drive resonant with the qubit transition frequency which is often theoretically described within the rotating-wave approximation (RWA). However, for fast gates on low-frequency qubits, the RWA may not hold and we need to consider the contribution from counter-rotating terms to the qubit dynamics. The inclusion of counter-rotating terms into the theoretical description gives rise to two challenges. Firstly, it becomes challenging to analytically calculate the time evolution as the Hamiltonian is no longer self-commuting. Moreover, the time evolution now depends on the carrier phase such that, in general, every operation in a sequence of gates is different. In this work, we derive and verify a correction to the drive pulses that minimizes the effect of these counter-rotating terms in a two-level system. We then derive a second correction term that arises from non-computational levels for a strongly anharmonic system. We experimentally implement these correction terms on a fluxonium superconducting qubit, which is an example of a strongly anharmonic, low-frequency qubit for which the RWA may not hold, and demonstrate how fast, high-fidelity single-qubit gates can be achieved without the need for additional hardware complexities.

We present a geometrical construction of driven quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over time. This results in a time-dependent quantum Hamiltonian with a structured temporal profile and properties dependent on the local and global nature of the underlying choice of manifold. We explain how our construction recovers the well-known classes of periodically-driven and quasiperiodically-driven quantum systems, but also unveils fundamentally novel classes of quantum dynamics: by steering a quantum Hamiltonian using a classical particle freely moving on a compact 2d hyperbolic Riemann surface called the Bolza surface, we demonstrate an example of a hyperbolically driven quantum system. We show that fully gapped hyperbolically driven quantum systems in the adiabatic limit are topologically classified by a quantized dynamical response. We propose geometric quantum driving to be a general framework to chart the landscape of time-dependent quantum systems, which can be realized with time-dependent controls available in modern day quantum simulators.

Unipolar light pulses with a non-zero electric area due to the unidirectional action on charged particles can be used for the ultrafast control of the properties of quantum systems. To control atomic properties in an efficient way, it is necessary to vary the temporal shape of the pulses used. This has led to the problem of obtaining pulses of an unusual shape, such as a rectangular one. A number of new phenomena, not possible with conventional multi-cycle pulses, were discovered by analyzing the interaction of such unipolar pulses with matter. These include the formation of dynamic microcavities at each resonant transition of a multilevel medium when such pulses collide with the medium. In this work, we compare the behavior of dynamic microcavities in a two-level and a three-level medium when unipolar pulses of unusual shape (rectangular) are collided with the medium. We do this on the basis of the numerical solution of the system for the density matrix of the medium and the wave equation for the electric field. Medium parameters correspond to atomic hydrogen. It is shown that for rectangular pulses in a three-level medium, the dynamics of the cavities can be very different from the two-level model, as opposed to pulses of other shapes (e.g. Gaussian shape). When the third level of the medium is taken into account, the self-induced transparency-like regime disappears. Differences in the dynamics of resonators in a three-level medium are revealed when the pulses behave like 2{\pi} pulses of self-induced transparency.

Recent demonstrations of D-Wave's annealing-based quantum simulators have established new benchmarks for quantum computational advantage [arXiv:2403.00910]. However, the precise location of the classical-quantum computational frontier remains an open question, as classical simulation strategies continue to evolve. Here, we demonstrate that time-dependent variational Monte Carlo (t-VMC) with a physically motivated Jastrow-Feenberg wave function can efficiently simulate the quantum annealing of spin glasses up to system sizes previously thought to be intractable. Our approach achieves accuracy comparable to that of quantum processing units while requiring only polynomially scaling computational resources, in stark contrast to entangled-limited tensor network methods that scale exponentially. For systems up to 128 spins on a three-dimensional diamond lattice, we maintain correlation errors below 7%, which match or exceed the precision of existing quantum hardware. Rigorous assessments of residual energies and time-dependent variational principle errors establish clear performance benchmarks for classical simulations. These findings substantially shift the quantum advantage frontier and underscore that classical variational techniques, which are not fundamentally constrained by entanglement growth, remain competitive at larger system sizes than previously anticipated.

We study the measurement of two-mode quantum correlations in the context of quantum key distribution (QKD) and quantum illumination (QI) through the detection of extracted work. We first observe that the extracted work, in units of $k_B T$, is identical for a two-mode squeezed thermal state (TMSTS) and a two-mode squeezed vacuum state (TMSVS). However, TMSTS exhibits $\bar{n}_{\rm th}$ times greater resistance to channel noise compared to TMSVS. We demonstrate that using TMSTS enhances the extracted work, joint-detection signal-to-noise ratio in QI, and correlation coefficients for QKD by approximately $\bar{n}_{\rm th}$ times relative to initializing the idler-signal system with a TMSVS. These findings highlight the potential of TMSTS for improving correlation detection in quantum protocols, with significant implications for noise resilience in QI and QKD.

Quantum systems under continuous weak measurement follow stochastic differential equations (SDE). Depending on the stochastic measurement results indeed, the quantum state can progressively diffuse, a priori in all directions of state space. This note draws attention to the observation that, in several settings of interest for quantum engineering, this diffusion in fact takes place in low dimension. Namely, the state remains confined in a low-dimensional nonlinear manifold, often time-dependent, but independent of the measurement results. The note provides the corresponding low-dimensional expressions for computing the stochastically evolving state in several such settings: quantum non-demolition measurement in arbitrary dimensions; quadrature measurements on a harmonic oscillator (linear quantum system); and subsystem measurement in multi-partite quantum systems. An algebraic criterion is proposed to directly check when such low-dimensional manifolds exist or survive under additional dynamics.

Quantum computing offers a promising route for tackling hard optimization problems by encoding them as Ising models. However, sparse qubit connectivity requires the use of minor-embedding, mapping logical qubits onto chains of physical qubits, which necessitates stronger intra-chain coupling to maintain consistency. This elevated coupling strength forces a rescaling of the Hamiltonian due to hardware-imposed limits on the allowable ranges of coupling strengths, reducing the energy gaps between competing states, thus, degrading the solver's performance. Here, we introduce a theoretical model that quantifies this degradation. We show that as the connectivity degree increases, the effective temperature rises as a polynomial function, resulting in a success probability that decays exponentially. Our analysis further establishes worst-case bounds on the energy scale degradation based on the inverse conductance of chain subgraphs, revealing two most important drivers of chain strength, \textit{chain volume} and \textit{chain connectivity}. Our findings indicate that achieving quantum advantage is inherently challenging. Experiments on D-Wave quantum annealers validate these findings, highlighting the need for hardware with improved connectivity and optimized scale-aware embedding algorithms.

We propose a novel optomechanical gyroscope architecture based on a spinning cavity optomechanical resonator (COM) evanescently coupled to a tapered optical fiber without relying on costly quantum light sources. Our study reveals a striking dependence of the gyroscope's sensitivity on the propagation direction of the driving optical field, manifesting robust quantum non-reciprocal behavior. This non-reciprocity significantly enhances the precision of angular velocity estimation, offering a unique advantage over conventional gyroscopic systems. Furthermore, we demonstrate that the operational range of this non-reciprocal gyroscope is fundamentally governed by the frequency of the pumping optical field, enabling localized sensitivity to angular velocity. Leveraging the adaptive capabilities of reinforcement learning (RL), we optimize the gyroscope's sensitivity within a targeted angular velocity range, achieving unprecedented levels of precision. These results highlight the transformative potential of RL in advancing high-resolution, miniaturized optomechanical gyroscopes, opening new avenues for next-generation inertial sensing technologies.

The notion of a macroscopic quantum state must be pinned down in order to assess how well experiments probe the large-scale limits of quantum mechanics. However, the issue of quantifying so-called quantum macroscopicity is fraught with multiple approaches having varying interpretations and levels of computability and measurability. Here, we introduce two measures that capture independent macroscopic properties: i) extensive size, measuring the degree of coherence in position or momentum observables relative to atomic-scale units, and ii) entangled size, quantifying the number of entangled subsystems. These measures unify many desirable features of past proposals while having rigorously justified interpretations from quantum information theory in terms of coherence and multipartite entanglement. We demonstrate how to estimate them and obtain lower-bounds using experimental data from micro-mechanical oscillators and diffracting molecules. Notably, we find evidence for genuine multipartite entanglement of $10^6$ to $10^7$ atoms in recent mechanical superposition states.

The NP-hardness of the closest vector problem (CVP) is an important basis for quantum-secure cryptography, in much the same way that integer factorisation's conjectured hardness is at the foundation of cryptosystems like RSA. Recent work with heuristic quantum algorithms (arXiv:2212.12372) indicates the possibility to find close approximations to (constrained) CVP instances that could be incorporated within fast sieving approaches for factorisation. This work explores both the practicality and scalability of the proposed heuristic approach to explore the potential for a quantum advantage for approximate CVP, without regard for the subsequent factoring claims. We also extend the proposal to include an antecedent "pre-training" scheme to find and fix a set of parameters that generalise well to increasingly large lattices, which both optimises the scalability of the algorithm, and permits direct numerical analyses. Our results further indicate a noteworthy quantum speed-up for lattice problems obeying a certain `prime' structure, approaching fifth order advantage for QAOA of fixed depth p=10 compared to classical brute-force, motivating renewed discussions about the necessary lattice dimensions for quantum-secure cryptosystems in the near-term.

The energy level degeneracies, also known as exceptional points (EPs), are crucial for comprehending emerging phenomena in materials and enabling innovative functionalities for devices. Since EPs were proposed over half a century age, only two types of EPs have been experimentally discovered, revealing intriguing phases of materials such as Dirac and Weyl semimetals. These discoveries have showcased numerous exotic topological properties and novel applications, such as unidirectional energy transfer. Here we report the observation of a novel type of EP, named the Dirac EP, utilizing a nitrogen-vacancy center in diamond. Two of the eigenvalues are measured to be degenerate at the Dirac EP and remain real in its vicinity. This exotic band topology associated with the Dirac EP enables the preservation of the symmetry when passing through, and makes it possible to achieve adiabatic evolution in non-Hermitian systems. We examined the degeneracy between the two eigenstates by quantum state tomography, confirming that the degenerate point is a Dirac EP rather than a Hermitian degeneracy. Our research of the distinct type of EP contributes a fresh perspective on dynamics in non-Hermitian systems and is potentially valuable for applications in quantum control in non-Hermitian systems and the study of the topological properties of EP.

We present a computation method to automatically design the n-qubit realisations of quantum algorithms. Our approach leverages a domain-specific language (DSL) that enables the construction of quantum circuits via modular building blocks, making it well-suited for evolutionary search. In this DSL quantum circuits are abstracted beyond the usual gate-sequence description and scale automatically to any problem size. This enables us to learn the algorithm structure rather than a specific unitary implementation. We demonstrate our method by automatically designing three known quantum algorithms--the Quantum Fourier Transform, the Deutsch-Jozsa algorithm, and Grover's search. Remarkably, we were able to learn the general implementation of each algorithm by considering examples of circuits containing at most 5-qubits. Our method proves robust, as it maintains performance across increasingly large search spaces. Convergence to the relevant algorithm is achieved with high probability and with moderate computational resources.

Secure Delegated Quantum Computation (SDQC) protocols allow a client to delegate a quantum computation to a powerful remote server while ensuring the privacy and the integrity of its computation. Recent resource-efficient and noise-robust protocols led to experimental proofs of concept. Yet, their physical requirements are still too stringent to be added directly to the roadmap of quantum hardware vendors. To address part of this issue, this paper shows how to alleviate the necessity for the client to have a single-photon source. It proposes a protocol that ensures that, among a sufficiently large block of transmitted weak coherent pulses, at least one of them was emitted as a single photon. This can then be used through quantum privacy amplification techniques to prepare a single secure qubit to be used in an SDQC protocol. As such, the obtained guarantee can also be used for Quantum Key Distribution (QKD) where the privacy amplification step is classical. In doing so, it proposes a workaround for a weakness in the security proof of the decoy state method. The simplest instantiation of the protocol with only 2 intensities already shows improved scaling at low transmittance and adds verifiability to previous SDQC proposals.

The concepts of $\epsilon$-nets and unitary ($\delta$-approximate) $t$-designs are important and ubiquitous across quantum computation and information. Both notions are closely related and the quantitative relations between $t$, $\delta$ and $\epsilon$ find applications in areas such as (non-constructive) inverse-free Solovay-Kitaev like theorems and random quantum circuits. In recent work, quantitative relations have revealed the close connection between the two constructions, with $\epsilon$-nets functioning as unitary $\delta$-approximate $t$-designs and vice-versa, for appropriate choice of parameters. In this work we improve these results, significantly increasing the bound on the $\delta$ required for a $\delta$-approximate $t$-design to form an $\epsilon$-net from $\delta \simeq \left(\epsilon^{3/2}/d\right)^{d^2}$ to $\delta \simeq \left(\epsilon/d^{1/2}\right)^{d^2}$. We achieve this by constructing polynomial approximations to the Dirac delta using heat kernels on the projective unitary group $\mathrm{PU}(d) \cong\mathbf{U}(d)$, whose properties we studied and which may be applicable more broadly. We also outline the possible applications of our results in quantum circuit overheads, quantum complexity and black hole physics.

Coherent nonlinear tripartite interactions are critical for advancing quantum simulation and information processing in hybrid quantum systems, yet they remain experimentally challenging and still evade comprehensive exploration. Here, we predict a nonlinear tripartite coupling mechanism in a hybrid setup comprising a single electron trapped on a solid neon surface and a nearby micromagnet. The tripartite coupling here leverages the electron's intrinsic charge (motional) and spin degrees of freedom interacting with the magnon modes of the micromagnet. Thanks to the large spatial extent of the electron zero-point motion, we show that it is possible to obtain a tunable and strong spin-magnon-motion coupling at the single quantum level, with two phonons simultaneously interacting with a single spin and magnon excitation. This enables, for example, dissipative interactions between the electron's charge and spin degrees of freedom, permitting controlled phonon addition/subtraction in the electron's motional state and the preparation of steady-state non-Gaussian motional states. This protocol can be readily implemented with the well-developed techniques in electron traps and may open new avenues for general applications in quantum simulations and information processing based on strongly coupled hybrid quantum systems.

Understanding the interplay between nonstabilizerness and entanglement is crucial for uncovering the fundamental origins of quantum complexity. Recent studies have proposed entanglement spectral quantities, such as antiflatness of the entanglement spectrum and entanglement capacity, as effective complexity measures, establishing direct connections to stabilizer R\'enyi entropies. In this work, we systematically investigate quantum complexity across a diverse range of spin models, analyzing how entanglement structure and nonstabilizerness serve as distinctive signatures of quantum phases. By studying entanglement spectra and stabilizer entropy measures, we demonstrate that these quantities consistently differentiate between distinct phases of matter. Specifically, we provide a detailed analysis of spin chains including the XXZ model, the transverse-field XY model, its extension with Dzyaloshinskii-Moriya interactions, as well as the Cluster Ising and Cluster XY models. Our findings reveal that entanglement spectral properties and magic-based measures serve as intertwined, robust indicators of quantum phase transitions, highlighting their significance in characterizing quantum complexity in many-body systems.

This thesis investigates the entanglement of distinguishable and indistinguishable particles, introducing a new error model for Hardy's test, experimentally verified using superconducting qubits. We address challenges in implementing quantum protocols based on this test and propose potential solutions and present two performance measures for qubits in superconducting quantum computers. We demonstrate that if quantum particles can create hyper-hybrid entangled states and achieve unit fidelity quantum teleportation, arbitrary state cloning is possible. This leads to two no-go theorems: hyper-hybrid entangled states cannot be formed with distinguishable particles, and unit fidelity quantum teleportation is unattainable with indistinguishable particles. These results establish unique correlations for each particle type, creating a clear distinction between the two domains. We also show that hyper-hybrid entangled states can be formed with indistinguishable fermions and generalize this for both fermions and bosons. We develop a generalized DoF trace-out rule applicable to single or multiple degrees of freedom for both types of particles. This framework allows us to derive expressions for teleportation fidelity and singlet fraction, establishing an upper bound for the generalized singlet fraction. We present an optical circuit that generates entanglement in distinguishable particles. Using our trace-out rule, we show that for two indistinguishable particles with multiple DoFs, the monogamy of entanglement can be maximally violated. We assert that indistinguishability is essential for this violation in qubit systems. For three indistinguishable particles, we confirm that monogamy is upheld using squared concurrence. Finally, we propose a novel entanglement swapping protocol involving two indistinguishable particles, enhancing quantum networks and quantum repeaters.

In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important instrument for quantum computing. Specifically, we summarize the application of tensor networks in various domains of quantum computing, including simulation of quantum computation, quantum circuit synthesis, quantum error correction, and quantum machine learning. Finally, we provide an outlook on the opportunities and the challenges of the tensor-network techniques.

Flux-tunable qubits and couplers are common components in superconducting quantum processors. However, dynamically controlling these elements via current pulses poses challenges due to distortions and transients in the propagating signals. In particular, long-time transients can persist, adversely affecting subsequent qubit control operations. We model the flux control line as a first-order RC circuit and introduce a class of pulses designed to mitigate long-time transients. We theoretically demonstrate the robustness of these pulses against parameter mischaracterization and provide experimental evidence of their effectiveness in mitigating transients when applied to a flux-tunable qubit coupler. The proposed pulse design offers a practical solution for mitigating long-time transients, enabling efficient and reliable experiment tune-ups without requiring detailed flux line characterization.

This study introduces a continuous-variable quantum neural network (CV-QNN) model designed as a transfer-learning approach for forecasting problems. The proposed quantum technique features a simple structure with only eight trainable parameters, a single quantum layer with two wires to create entanglement, and ten quantum gates, hence the name QNNet10, effectively mimicking the functionality of classical neural networks. A notable aspect is that the quantum network achieves high accuracy with random initialization after a single iteration. This pretrained model is innovative as it requires no training or parameter tuning when applied to new datasets, allowing for parameter freezing while enabling the addition of a final layer for fine-tuning. Additionally, an equivalent discrete-variable quantum neural network (DV-QNN) is presented, structured similarly to the CV model. However, analysis shows that the two-wire DV model does not significantly enhance performance. As a result, a four-wire DV model is proposed, achieving comparable results but requiring a larger and more complex structure with additional gates. The pretrained model is applied to five forecasting problems of varying sizes, demonstrating its effectiveness.

Quantum technologies are increasingly pervasive, underpinning the operation of numerous electronic, optical and medical devices. Today, we are also witnessing rapid advancements in quantum computing and communication. However, access to quantum technologies in computation remains largely limited to professionals in research organisations and high-tech industries. This paper demonstrates how traditional neural networks can be transformed into neuromorphic quantum models, enabling anyone with a basic understanding of undergraduate-level machine learning to create quantum-inspired models that mimic the functioning of the human brain -- all using a standard laptop. We present several examples of these quantum machine learning transformations and explore their potential applications, aiming to make quantum technology more accessible and practical for broader use. The examples discussed in this paper include quantum-inspired analogues of feedforward neural networks, recurrent neural networks, Echo State Network reservoir computing and Bayesian neural networks, demonstrating that a quantum approach can both optimise the training process and equip the models with certain human-like cognitive characteristics.

$^4$He nanodroplets doped with an alkali ion feature a snowball of crystallized layers surrounded by superfluid helium. For large droplets, we predict that a transitional supersolid layer can form, bridging between the solid core and the liquid bulk, where the $^4$He density displays modulations of icosahedral group symmetry. To identify the different phases, we combine density functional theory with the semiclassical Gaussian time-dependent Hartree method for localized many-body systems. This hybrid approach can handle large particle numbers and provides insight into the physical origin of the supersolid layer. For small droplets, we verify that the predictions of our approach are in excellent agreement with Path-Integral Monte Carlo calculations.

We demonstrate the existence of transient two-dimensional surfaces where a random-walking particle escapes to infinity in contrast to localization in standard flat 2D space. We first prove that any rotationally symmetric 2D membrane embedded in flat 3D space cannot be transient. Then we formulate a criterion for the transience of a general asymmetric 2D membrane. We use it to explicitly construct a class of transient 2D manifolds with a non-trivial metric and height function but ``zero average curvature,'' which we dub tablecloth manifolds. The absence of the logarithmic infrared divergence of the Laplace-Beltrami operator in turn implies the absence of weak localization, non-existence of bound states in shallow potentials, and breakdown of the Mermin-Wagner theorem and Kosterlitz-Thouless transition on the tablecloth manifolds, which may be realizable in both quantum simulators and corrugated two-dimensional materials.

The search for non-Abelian anyons in quantum spin liquids (QSLs) is crucial for advancing fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, nonmagnetic spin vacancies are known to bind emergent gauge fluxes of the QSL ground state, which in turn become non-Abelian anyons for an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons at spin vacancies extends to a finite magnetic field represented by a proper Zeeman term. Specifically, we use large-scale density-matrix renormalization group (DMRG) simulations to compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic (FM) and antiferromagnetic (AFM) Kitaev models. We find that, while the inclusion of the field weakens anyon binding in both cases, there is a pronounced difference in the finite-field behavior; the binding energy remains finite within the entire QSL phase for the FM Kitaev model but approaches zero already inside this phase for the AFM Kitaev model. To reliably compute a very small binding energy that is three orders of magnitude below the magnetic interaction strength, we also introduce a refined definition for the binding energy and an extrapolation scheme for its accurate extraction through exclusively ground-state properties using DMRG.

Entanglement entropy is a fundamental measure of quantum entanglement for pure states, but for large-scale many-body systems, R\'{e}nyi entanglement entropy is much more computationally accessible. For mixed states, logarithmic negativity (LN) serves as a widely used entanglement measure, but its direct computation is often intractable, leaving R\'{e}nyi negativity (RN) as the practical alternative. In fermionic systems, RN is further classified into untwisted and twisted types, depending on the definition of the fermionic partial transpose. However, which of these serves as the true R\'{e}nyi proxy for LN has remained unclear -- until now. In this work, we address this question by developing a robust quantum Monte Carlo (QMC) method to compute both untwisted and twisted RNs, focusing on the rank-4 twisted RN, where non-trivial behavior emerges. We identify and overcome two major challenges: the singularity of the Green's function matrix and the exponentially large variance of RN estimators. Our method is demonstrated in the Hubbard model and the spinless $t$-$V$ model, revealing critical distinctions between untwisted and twisted RNs, as well as between rank-2 and high-rank RNs. Remarkably, we find that the twisted R\'{e}nyi negativity ratio (RNR) adheres to the area law and decreases monotonically with temperature, in contrast to the untwisted RNR but consistent with prior studies of bosonic systems. This study not only establishes the twisted RNR as a more pertinent R\'{e}nyi proxy for LN in fermionic systems but also provides comprehensive technical details for the stable and efficient computation of high-rank RNs. Our work lays the foundation for future studies of mixed-state entanglement in large-scale fermionic many-body systems.

We introduce a model of an active quantum particle and discuss its properties. The particle has a set of internal states that mediate exchanges of heat with external reservoirs. Heat is then converted into motion by means of a spin-orbit term that couples internal and translational degrees of freedom. The quantum features of the active particle manifest both in the motion and in the heat-to-motion conversion. Furthermore, the stochastic nature of heat exchanges impacts the motion of the active particle and fluctuations can be orders of magnitude larger than the average values. The combination of spin-orbit interaction under nonequilibrium driving may bring active matter into the realm of cold atomic gases where our proposal can be implemented.

We undertake a Shannon theoretic study of the problem of communicating classical information over a $3-$user quantum interference channel (QIC) and focus on characterizing inner bounds. In our previous work, we had demonstrated that coding strategies based on coset codes can yield strictly larger inner bounds. Adopting the powerful technique of \textit{tilting}, \textit{smoothing} and \textit{augmentation} discovered by Sen recently, and combining with our coset code strategy we derive a new inner bound to the classical-quantum capacity region of a $3-$user QIC. The derived inner bound subsumes all current known bounds.

We present a universal parameter-free quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than $1/2$) Hamiltonians. This approach extends a previously developed method by the authors for spin-$1/2$ Hamiltonians [Phys. Rev. Research 6, 013281 (2024)]. To demonstrate its applicability and versatility, we apply our method to the spin-$1$ and spin-$3/2$ quantum Heisenberg models on the square lattice. Additionally, we detail how the approach naturally extends to general Hamiltonians involving mixtures of particle species, including bosons and fermions. We have made our program code freely accessible on GitHub.

The structural, thermoelectric, and optical properties of $[NH_3-(CH_2)_4-NH_3]CdCl_4$ were studied using Density Functional Theory (DFT) within the ABINIT code. The GGA-PBE functional, plane wave pseudopotentials, a kinetic energy cutoff of $35Ha$, and an 11x8x8 Monkhorst-Pack $k$-point grid were employed. The material comprises inorganic $[CdCl_4]^{2-}$ sheets, organic $[NH_3-(CH_2)_4-NH_3]^{2+}$ layers, and $N-H-Cl$ hydrogen bonds, ensuring sublattice cohesion. Structural optimization used reference crystal data, enabling analysis of alkylene-diammonium chain conformation, intermolecular interactions, and crystal stability. The study highlights the role of $Cd$ in influencing optical and thermoelectric properties. Temperature-induced changes lead to a reduced band gap and enhanced optical absorption, indicating significant electronic structure modifications. These findings propose $[NH_3-(CH_2)_4-NH_3]CdCl_4$ as a promising candidate for optoelectronic applications, particularly after thermal cycling, due to its improved performance under varying conditions.

The Kohn-Sham (KS) density matrix is one of the most essential properties in KS density functional theory (DFT), from which many other physical properties of interest can be derived. In this work, we present a parameterized representation for learning the mapping from a molecular configuration to its corresponding density matrix using the Atomic Cluster Expansion (ACE) framework, which preserves the physical symmetries of the mapping, including isometric equivariance and Grassmannianity. Trained on several typical molecules, the proposed representation is shown to be systematically improvable with the increase of the model parameters and is transferable to molecules that are not part of and even more complex than those in the training set. The models generated by the proposed approach are illustrated as being able to generate reasonable predictions of the density matrix to either accelerate the DFT calculations or to provide approximations to some properties of the molecules.

Purpose: To develop 5T-SRIS, an improved 5T myocardial T1 mapping method based on MOLLI, which addresses limitations in inversion efficiency, readout perturbations, and imperfect magnetization recovery. Methods: The proposed 5T-SRIS method is based on a modified 5-(3)-3 MOLLI sequence with ECG gating and gradient echo readout. To improve inversion efficiency at 5T, the inversion pulse was redesigned using adiabatic hyperbolic secant (HSn) and tangent/hyperbolic tangent (Tan/Tanh) pulses. Signal evolution was modeled recursively with inversion efficiency and a correction factor (C) to correct inversion imperfections, and T1 values were estimated via nonlinear optimization. The method was validated in phantom studies, as well as in 21 healthy volunteers and 9 patients at 5T. Results: The optimized IR pulse based on the tangent/hyperbolic tangent pulse was found to outperform the conventional hyperbolic secant IR pulse at the 5T scanner. This optimized IR pulse achieves an average inversion factor of 0.9014within a B0 range of 250Hz and a B1 range of -50% to 20%. Phantom studies show that the 5T-SRIS achieved high accuracy with errors within 5%. In vivo studies with 21 healthy volunteers, the native myocardial T1 values were 1468 ms (apex), 1514 ms (middle), and 1545 ms (base). In vivo studies with 9 heart patients, the native myocardial T1 values were 1484 ms (apex), 1532 ms (middle), and 1581 ms (base). And the post myocardial T1 values were 669 ms (apex), 698 ms (middle), and 675 ms (base). Conclusion: The 5T-SRIS technique is robust and suitable for clinical cardiac imaging. This study demonstrates its feasibility for accurate myocardial T1 mapping at 5T, despite challenges related to magnetic field inhomogeneity. Keywords: Myocardial T1 mapping, 5T, improved MOLLI, 5T-SRIS

We present a fully numerical framework for the optimization of molecule-specific quantum chemical basis functions within the quantics tensor train format using a finite-difference scheme. The optimization is driven by solving the Hartree-Fock equations (HF) with the density-matrix renormalization group (DMRG) algorithm on Cartesian grids that are iteratively refined. In contrast to the standard way of tackling the mean-field problem by expressing the molecular orbitals as linear combinations of atomic orbitals (LCAO) our method only requires as much basis functions as there are electrons within the system. Benchmark calculations for atoms and molecules with up to ten electrons show excellent agreement with LCAO calculations with large basis sets supporting the validity of the tensor network approach. Our work therefore offers a promising alternative to well-established HF-solvers and could pave the way to define highly accurate, fully numerical, molecule-adaptive basis sets, which, in the future, could lead to benefits for post-HF calculations.

Vortex states of photons or electrons are a novel and promising experimental tool across atomic, nuclear, and particle physics. Various experimental schemes to generate high-energy vortex particles have been proposed. However, diagnosing the characteristics of vortex states at high energies remains a significant challenge, as traditional low-energy detection schemes become impractical for high-energy vortex particles due to their extremely short de Broglie wavelength. We recently proposed a novel experimental detection scheme based on a mechanism called "superkick" that is free from many drawbacks of the traditional methods and can reveal the vortex phase characteristics. In this paper, we present a complete theoretical framework for calculating the superkick effect in elastic electron scattering and systematically investigate the impact of various factors on its visibility. In particular, we argue that the vortex phase can be identified either by detecting the two scattered electrons in coincidence or by analyzing the characteristic azimuthal asymmetry in individual final particles.

In this letter, we report the magneto-electronic properties of high mobility InAs quantum point contacts grown on InP substrates. The 1D conductance reaches a maximum value of 17 plateaus, quantized in units of 2e^2/h, where e is the fundamental unit of charge and h is Planck's constant. The in-plane effective g-factor was estimated to be -10.9 +/- 1.5 for subband N = 1 and -10.8 +/- 1.6 for subband N = 2. Furthermore, a study of the non-magnetic fractional conductance states at 0.2 (e^2/h) and 0.1(e2/h is provided. While their origin remains under discussion, evidence suggests that they arise from strong electron-electron interactions and momentum-conserving backscattering between electrons in two distinct channels within the 1D region. This phenomenon may also be interpreted as an entanglement between the two channel directions facilitated by momentum-conserving backscattering.

Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo field dynamics (TFD) and the Schwinger-Keldysh formalism. In this article, we provide a more detailed discussion of these methods and derive expressions for density matrix elements of closed and open systems. At first, we look at closed systems by discussing general solutions to the Schr\"odinger-like form of the quantum Liouville equations in TFD, showing that the dynamical map is indeed divisible, deriving a path integral-based expression for the density matrix elements in Fock space, and explaining why perturbation theory enables us to use the last even in situations where all initial states in Fock space are occupied. Subsequently, we discuss open systems in the same manner after tracing out environmental degrees of freedom from the solutions for closed systems. We find that, even in a general basis, the dynamical map is not divisible, which renders the dynamics of open systems non-Markovian. Finally, we show how the resulting expressions for open systems can be used to obtain quantum master equations, and comment on the artificiality of time integrals over density matrices that usually appear in many other master equations in the literature but are absent in ours.