Daily Papers

We investigate the effects of quantum geometry on the motion of magnon wave packets in one-dimensional quantum spin chains. In contrast to fermionic systems, where transport phenomena driven by the quantum metric have been extensively studied, we show that the dynamics in bosonic magnon systems are strongly affected by the symplectic structure and the pseudo-unitarity of the transformation of the magnon Bogoliubov-de Gennes Hamiltonian. A chiral soliton lattice provides a setting in which the symplectic quantum metric strongly influences the longitudinal magnon dynamics. We derive the semiclassical response of a magnon wave packet in such a system to a weak, slowly varying perturbation and demonstrate that the wave packet velocity acquires a geometric contribution proportional to the momentum derivative of the symplectic quantum metric, which dominates over the conventional group velocity for a nearly flat band. Solving the resulting equations of motion, we obtain a bounded trajectory in real time with a phase-space area determined by the symplectic quantum metric.

We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics. The derivation of quantization rules and energy levels is revisited using semiclassical methods. Sommerfeld-type integrals are evaluated by elementary techniques, and connections with the Schr\"{o}dinger and Dirac equations are established. Historical developments and key transitions from classical to quantum theory are discussed to clarify the structure and significance of the old quantum mechanics.

Let P_h be a semiclassical pseudodifferential operator on a closed Riemannian manifold (M,g), with principal symbol p. We consider perturbations P_h+h^αQ, with 0<αle 1, where Q is a semiclassical pseudodifferential operator whose symbol oscillates at scale h^β, with 2β<α. Assuming that the classical dynamics of the unperturbed system on a regular energy surface p^{-1}(E) is hyperbolic, we prove a Gutzwiller trace formula for the perturbed operator that holds up to times of order |log h|. This formula relates the distribution of energy levels of the quantum system near the energy E to the periodic orbits of its classical counterpart. The perturbation h^αQ affects only the phases appearing in the trace formula.

We study, within a toy model, how a thermal bath of cosmological perturbations can decohere the minisuperspace degrees of freedom of the universe, treating the perturbations as an environment in the framework of open quantum systems. Instead of tracing out the perturbations from a semiclassical ansatz for the total wave function, as in earlier approaches, we incorporate their backreaction on the background through an effective second-order coupling and derive a master equation. The model describes a spatially flat semiclassical universe during slow-roll inflation with a dust clock field, while scalar cosmological perturbations in a phenomenologically assumed thermal state constitute the environment. The master equation is non-Markovian, since the bath correlation functions do not decay in time. Within this framework, we find that, for a representative set of parameter estimates, the characteristic decoherence timescale corresponding to the thermal contribution can be shorter than the Hubble timescale. In addition, we address the question of whether the pointer-state structure induced by the decoherence in such a framework could provide a criterion for the choice of semiclassical states in quantum cosmology.

We consider fermions in a zero-temperature superconducting anti-de Sitter domain wall solution and find continuous bands of normal modes. These bands can be either partially filled or totally empty and gapped. We present a semi-classical argument which approximately captures the main features of the normal mode spectrum.

We establish lower bounds on the number of resonances for three-dimensional semiclassical Dirac operators with mass-type potentials. For a pair Dl_j=Dl_0+mbfβv_j, j=1,2, satisfying the exterior analyticity, decay and non-degeneracy assumptions of the paper, we associate a relative distribution μ to the corresponding mass functions. We prove that if E_0>1 is a boundary point of suppμ, then every complex neighbourhood of E_0, and likewise of -E_0, contains in total at least Chbar^{-3} resonances of the two operators, counted with multiplicity. The proof transfers an analytic wave-front singularity of μ to the relative classical density of states and combines this with Khochman's local trace formula and a relative semiclassical trace formula. As a consequence, if v is a single bounded mass-type potential, analytic with power decay in an exterior sector, with inf(1+v)>0 and sup v>0, then Dl=Dl_0+mbfβv has at least Chbar^{-3} resonances in every complex neighbourhood of E_0=1+sup v and of -E_0, for all sufficiently small hbar. The exponent agrees with Khochman's upper bound, the two resonance families are related by spectral symmetry, and E_0 is necessarily a trapping energy. We also prove the relative semiclassical trace formula needed in the argument for general Hermitian matrix-valued perturbations.

The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space the conformal dimension Delta (Q) of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q. This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups. Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in different dimensions. We analyze the convexity properties of the leading and next-to-leading order terms stemming from the semiclassical computation, de facto, extending previous tests beyond the leading perturbative contributions and to arbitrary charges. In particular, the leading contribution is sufficient to test convexity in the semiclassical computations. We also consider intriguing cases in which the models feature a transition from real to complex conformal dimensions either as a function of the charge or number of matter fields. As a relevant example of the first kind, we investigate the O(N) model in 4+epsilon dimensions. As an example of the second type we consider the U(N)times U(M) model in 4-epsilon dimensions. Both models display a rich dynamics where, by changing the number of matter fields and/or charge, one can achieve dramatically different physical regimes. We discover that whenever a complex conformal dimension appears, the real part satisfies the convexity property.

We investigate the spectral statistics of random perturbations of semiclassical Schrödinger operators on compact manifolds, near energy levels corresponding to chaotic classical dynamics. The prototypical example is that of an operator h^2Δ+V(x) that is perturbed by a smooth potential h^αV_ω with αin (0,1), and V_ω is a random potential that decorrelates on distances h^β, with 0<β<2α. We show that for a generic perturbation, the spectral fluctuations of the smoothed counting function of eigenvalues obey a universal behavior at a certain mesoscopic scale, which is coherent with the predictions of random matrix theory.

We study resonance expansions and localised long-time dynamics for three-dimensional semiclassical Dirac operators. For smooth Hermitian matrix-valued perturbations which are analytic outside a compact set, we first obtain exponential cut-off resolvent bounds away from the resonance set and polynomial bounds in thin resonance-free rectangles adjacent to the real axis. Combining these estimates with a local Oc(h^{-3}) upper bound on the number of resonances, a pigeonhole selection of admissible contours, almost-analytic functional calculus, and a Cauchy--Green deformation, we derive resonance expansions for spectrally localised propagators. Positive-energy resonances contribute for large positive times, whereas negative-energy resonances contribute for large negative times. We then specialise to mass-type perturbations mbfβV(x) in a nontrapping energy window. Using the logarithmic resonance-free region established in our earlier work together with a quantitative FBI-transform/escape-function argument, we obtain a polynomial bound for the continued cut-off resolvent and deduce rapid local-energy decay. We subsequently refine this polynomial estimate by a finite-time propagation argument in the undistorted region. Introducing the maximal positive-sheet connection time T_χ associated with the spatial cutoff, we prove a geometric continued-resolvent estimate and, for every fixed M below the resonance-free depth constant, derive the explicit local-energy decay threshold T_N>T_χ+(N+1)/M. The same analysis gives a rigorous microlocal obstruction to a uniform [hlog(1/h)]^{-1} bound for the full distorted resolvent and identifies a finite-flight-time amplification mechanism for the sandwiched continued resolvent at logarithmic depth.

Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems. The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities. The third lecture presents transport coefficients derived from AdS/CFT that should be applicable in the quantum critical region associated to a quantum phase transition. The fourth lecture builds in the physics of a superconducting or superfluid phase transition to the simple holographic model of the third lecture.

We give an overview of the light-front holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higher-dimensional anti de Sitter (AdS) space. The framework is guided by the AdS/CFT correspondence incorporating a gravitational background asymptotic to AdS space which encodes the salient properties of QCD, such as the ultraviolet conformal limit at the AdS boundary at z to 0, as well as modifications of the geometry in the large z infrared region to describe confinement and linear Regge behavior. There are two equivalent procedures for deriving the AdS/QCD equations of motion: one can start from the Hamiltonian equation of motion in physical space time by studying the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a light-front Hamiltonian equation which describes the bound state dynamics of light hadrons in terms of an invariant impact variable ζ which measures the separation of the partons within the hadron at equal light-front time. Alternatively, one can start from the gravity side by studying the propagation of hadronic modes in a fixed effective gravitational background. Both approaches are equivalent in the semiclassical approximation. This allows us to identify the holographic variable z in AdS space with the impact variable ζ. Light-front holography thus allows a precise mapping of transition amplitudes from AdS to physical space-time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.

Symmetry has long provided the organizing principle for understanding how materials respond to external perturbations. Here we show that what is permitted by symmetry need not be what actually emerges from the underlying system, and this distinction becomes particularly consequential for symmetry-related gapless Dirac fermions such as in altermagnets. A perturbation that shifts the Dirac points drives a Lifshitz reconstruction and generates an intrinsically nonanalytic effective potential, giving rise to undiscovered singular responses. In Dirac altermagnets, this nonanalyticity acquires a magnetic manifestation through C-paired spin-polarized Dirac cones: breaking the pairing symmetry C lifts their degeneracy and converts the associated Lifshitz reconstruction into an itinerant magnetization. As a consequence, piezomagnetism, the induction of a net magnetization by a mechanical strain, becomes nonlinear and nonanalytic, with Mproptosgn(varepsilon)varepsilon^2, whereas the linear response is absent despite being allowed by symmetry. Accordingly, the leading response cannot be inferred from the conventional symmetry-based paradigm of material response built upon the cornerstones of Neumann's principle and analytic Landau expansion. First-principles calculations identify the monolayer Fe_2S as a candidate material realization for such singular magnetic responses. These results suggest quantum singularities as a new degree of freedom for engineering material responses.

Quantum Zeno Effect (QZE) has been one of the most interesting phenomena in quantum mechanics ever since its discovery in 1977 by Misra and Sudarshan [J. Math. Phys. 18, 756 (1977)]. There have been many attempts for experimental realization of the same. Here, we present the first ever simulation of QZE on IBM quantum experience platform. We simulate a two-level system for Rabi-driven oscillation and then disturb the time evolution by intermediate repetitive measurements using quantum gates to increase the survival probability of the qubit in the initial state. The circuits are designed along with the added intermediate measurements and executed on IBM quantum simulator, and the outcomes are shown to be consistent with the predictions. The increasing survival probability with the number of intermediate measurements demonstrates QZE. Furthermore, some alternative explanations for the obtained results are provided which leads to some ambiguity in giving the exact reasoning for the observed outcomes.

The study of the long-time dynamics of quantum systems can be a real challenge, especially in systems like ultracold gases, where the required timescales may be longer than the lifetime of the system itself. In this work, we show that it is possible to access the long-time dynamics of a strongly repulsive atomic gas mixture in shorter times. The shortcut-to-dynamics protocol that we propose does not modify the fate of the observables, but effectively jumps ahead in time without changing the system's inherent evolution. Just like the next-chapter button in a movie player that allows to quickly reach the part of the movie one wants to watch, it is a leap into the future.

We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an Ntimes N matrix M, an N-dimensional vector emph{b}, and an initial vector emph{x}(0), obtain a target vector emph{x}(t) as a function of time t according to the constraint demph{x}(t)/dt=Memph{x}(t)+emph{b}. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a 4times4 linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations.

Wentzel, Kramers, Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case the wave function is constructed such that the phase factor is the same as the Hamilton's principle function "S". To demonstrate our proposed approach two examples are investigated in details.

Critical phenomena of quantum systems are useful for enhancement of quantum sensing. However, experimental realizations of criticality enhancement have been confined to very few systems, owing to the stringent requirements, including the thermodynamical or scaling limit, and fine control of interacting quantum susystems or particles. We here propose a simple critical quantum sensing scheme that requires neither of these conditions. The critical system is realized with a single parametrically-driven bosonic mode involving many non-interacting bosons. We calculate the quantum Fisher information, and perform a simulation, which confirms the criticality-enabled enhancement. We further detail the response of one of the quadratures to the variation of the control parameter. The numerical results reveal that its inverted variance exhibits a diverging behavior at the critical point. Based on the presently available control techniques of parametric driving, we expect our scheme can be realized in different systems, e.g., ion traps and superconducting circuits.

In the BCS theory of superconductivity the amplitude (Higgs) mode is degenerate with the pair-breaking threshold: its frequency coincides with 2Δ, so it is an edge singularity rather than a true collective mode. This is why after a sudden weak perturbation at t=0 its oscillations decay algebraically as 1/t. We show that the retardation effects due to the phonon dynamics in the strong-coupling theory lift this degeneracy. The Higgs mode detaches from the pair-breaking edge 2Δ_g, set by the spectral gap, and becomes a sharp subgap excitation. We determine its frequency from the longitudinal pair susceptibility evaluated directly on the real frequency axis, using the Eilenberger equations for Migdal--Eliashberg theory with the Einstein phonon spectrum. The response of the mass renormalization supplies at least two fifths of the displacement, and possibly all of it: with it switched off, the binding falls below the resolution of the calculation. Its consequences, however, are significant because a percent-level shift transfers about a quarter of the spectral weight of the amplitude channel out of the two-quasiparticle continuum into a discrete energy level. What experiment sees is therefore not the displacement itself but its consequence: amplitude oscillations that persist instead of decaying as 1/t.

We consider an experimentally obtainable SUP operator, defined by using a generalized superposition of products of field annihilation (a) and creation (a^dagger) operators of the type, A = saa^dagger+t{a^dagger}a with s^2+t^2=1. We apply this SUP operator on coherent and thermal quantum states, the states thus produced are referred as SUP-operated coherent state (SOCS) and SUP-operated thermal state (SOTS), respectively. In the present work, we report a comparative study between the higher-order nonclassical properties of SOCS and SOTS. The comparison is performed by using a set of nonclassicality witnesses (e.g., higher-order antiubunching, higher-order sub-Poissonian photon statistics, higher-order squeezing, Agarwal-Tara parameter, Klyshko's condition). The existence of higher-order nonclassicalities in SOCS and SOTS have been investigated for the first time. In view of possible experimental verification of the proposed scheme, we present exact calculations to reveal the effect of non-unit quantum efficiency of quantum detector on higher-order nonclassicalities.

Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers all times. The quantum formalism arises once one focuses on the evolution of the time-local probabilistic information. Wave functions or the density matrix allow the formulation of a general linear evolution law for classical statistics. The quantum formalism for classical statistics is a powerful tool which allows us to implement for generalized Ising models the momentum observable with the associated Fourier representation. The association of operators to observables permits the computation of expectation values in terms of the density matrix by the usual quantum rule. We show that probabilistic cellular automata are quantum systems in a formulation with discrete time steps and real wave functions. With a complex structure the evolution operator for automata can be expressed in terms of a Hamiltonian involving fermionic creation and annihilation operators. The time-local probabilistic information amounts to a subsystem of the overall probabilistic system which is correlated with its environment consisting of the past and future. Such subsystems typically involve probabilistic observables for which only a probability distribution for their possible measurement values is available. Incomplete statistics does not permit to compute classical correlation functions for arbitrary subsystem-observables. Bell's inequalities are not generally applicable.

In image processing, the amount of data to be processed grows rapidly, in particular when imaging methods yield images of more than two dimensions or time series of images. Thus, efficient processing is a challenge, as data sizes may push even supercomputers to their limits. Quantum image processing promises to encode images with logarithmically less qubits than classical pixels in the image. In theory, this is a huge progress, but so far not many experiments have been conducted in practice, in particular on real backends. Often, the precise conversion of classical data to quantum states, the exact implementation, and the interpretation of the measurements in the classical context are challenging. We investigate these practical questions in this paper. In particular, we study the feasibility of the Flexible Representation of Quantum Images (FRQI). Furthermore, we check experimentally what is the limit in the current noisy intermediate-scale quantum era, i.e. up to which image size an image can be encoded, both on simulators and on real backends. Finally, we propose a method for simplifying the circuits needed for the FRQI. With our alteration, the number of gates needed, especially of the error-prone controlled-NOT gates, can be reduced. As a consequence, the size of manageable images increases.

With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to be no. A certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer. Based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element. The concept that this is solely a quantum effect and does not work for a classical case is also discussed.

Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantum computing. The paper begins by motivating the central ideas of quantum mechanics and quantum computation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite dimensional) quantum mechanics that we will need for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simplest quantum algorithms: Deutsch's algorithm. Our presentation demands neither advanced mathematics nor advanced physics.

We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is benchmarked against state-of-the-art techniques, showing a remarkable acceleration. As a side product, we provide an optimized method for one key calculus in quantum simulations: the Pauli basis decomposition of Hamiltonians.

The energy levels of hydrogen-like atoms are obtained from the phase-space quantization, one of the pillars of the old quantum theory, by three different methods - (i) direct integration, (ii) Sommerfeld's original method, and (iii) complex integration. The difficulties come from the imposition of elliptical orbits to the electron, resulting in a variable radial component of the linear momentum. Details of the calculation, which constitute a recurrent gap in textbooks that deal with phase-space quantization, are shown in depth in an accessible fashion for students of introductory quantum mechanics courses.

Previous theoretical and experimental research has shown that current NISQ devices constitute powerful platforms for analogue quantum simulation. With the exquisite level of control offered by state-of-the-art quantum computers, we show that one can go further and implement a wide class of Floquet Hamiltonians, or timedependent Hamiltonians in general. We then implement a single-qubit version of these models in the IBM Quantum Experience and experimentally realize a temporal version of the Bernevig-Hughes-Zhang Chern insulator. From our data we can infer the presence of a topological transition, thus realizing an earlier proposal of topological frequency conversion by Martin, Refael, and Halperin. Our study highlights promises and limitations when studying many-body systems through multi-frequency driving of quantum computers.

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang's breakthrough quantum-inspired algorithm for recommendation systems [STOC'19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén, Su, Low, and Wiebe [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all recent results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ell^2-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical foundations of this link and show how it opens up a new avenue for the design of quantum machine learning algorithms. We interpret the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space. A quantum computer can now analyse the input data in this feature space. Based on this link, we discuss two approaches for building a quantum model for classification. In the first approach, the quantum device estimates inner products of quantum states to compute a classically intractable kernel. This kernel can be fed into any classical kernel method such as a support vector machine. In the second approach, we can use a variational quantum circuit as a linear model that classifies data explicitly in Hilbert space. We illustrate these ideas with a feature map based on squeezing in a continuous-variable system, and visualise the working principle with 2-dimensional mini-benchmark datasets.

We study the electromagnetic field equations on an arbitrary quantum curved background in the semiclassical approximation of Loop Quantum Gravity. The effective interaction hamiltonian for the Maxwell and gravitational fields is obtained and the corresponding field equations, which can be expressed as a modified wave equation for the Maxwell potential, are derived. We use these results to analyze electromagnetic wave propagation on a quantum Robertson-Walker space time and show that Lorentz Invariance is not preserved. The formalism developed can be applied to the case where back reaction effects on the metric due to the electromagnetic field are taken into account, leading to non covariant field equations.

We present a web-based software tool, the Virtual Quantum Optics Laboratory (VQOL), that may be used for designing and executing realistic simulations of quantum optics experiments. A graphical user interface allows one to rapidly build and configure a variety of different optical experiments, while the runtime environment provides unique capabilities for visualization and analysis. All standard linear optical components are available as well as sources of thermal, coherent, and entangled Gaussian states. A unique aspect of VQOL is the introduction of non-Gaussian measurements using detectors modeled as deterministic devices that "click" when the amplitude of the light falls above a given threshold. We describe the underlying theoretical models and provide several illustrative examples. We find that VQOL provides a a faithful representation of many experimental quantum optics phenomena and may serve as both a useful instructional tool for students as well as a valuable research tool for practitioners.

In this paper, we examine the thermodynamic behavior of a quantum harmonic oscillator with a position-dependent mass (PDM), where spatial inhomogeneity is modeled through a deformation parameter α. Based on the exact energy spectrum, we explore the resulting thermodynamic quantities and superstatistics. Our findings reveal that increasing α leads to a decrease in entropy and specific heat, reflecting a confinement-induced reduction in the number of accessible states. The partition function and free energy exhibit smooth behavior across all parameter regimes, indicating the absence of critical phase transitions. This study underscores the influence of mass deformation on quantum thermal responses and demonstrates that, while the overall thermodynamic trends are consistent with those reported in the literature, certain distinctive features emerge due to the specific form of the deformation.

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We present strong evidence that commonly used models with provable absence of barren plateaus are also classically simulable, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing quantum computers can be essential for collecting data, our analysis sheds serious doubt on the non-classicality of the information processing capabilities of parametrized quantum circuits for barren plateau-free landscapes. We end by discussing caveats in our arguments, the role of smart initializations and the possibility of provably superpolynomial, or simply practical, advantages from running parametrized quantum circuits.

We give a classical analogue to Kerenidis and Prakash's quantum recommendation system, previously believed to be one of the strongest candidates for provably exponential speedups in quantum machine learning. Our main result is an algorithm that, given an m times n matrix in a data structure supporting certain ell^2-norm sampling operations, outputs an ell^2-norm sample from a rank-k approximation of that matrix in time O(poly(k)log(mn)), only polynomially slower than the quantum algorithm. As a consequence, Kerenidis and Prakash's algorithm does not in fact give an exponential speedup over classical algorithms. Further, under strong input assumptions, the classical recommendation system resulting from our algorithm produces recommendations exponentially faster than previous classical systems, which run in time linear in m and n. The main insight of this work is the use of simple routines to manipulate ell^2-norm sampling distributions, which play the role of quantum superpositions in the classical setting. This correspondence indicates a potentially fruitful framework for formally comparing quantum machine learning algorithms to classical machine learning algorithms.

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms were recently tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW'19 paper on QSVT [Gily\'en, Su, Low, and Wiebe, ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which QSVT naturally emerges. Paralleling GSLW'19, we then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how QSVT is a single framework comprising the three major quantum algorithms, thus suggesting a grand unification of quantum algorithms.

Adopting general frameworks for quantum-classical dynamics, we analyze the interaction between quantum matter and a classical gravitational field. We point out that, assuming conservation of momentum or energy, and assuming that the dynamics obeys Hamiltonian formalism or a particular decomposition property set out in the paper, the classical gravitational field cannot change the momentum or energy of the quantum system, whereas the quantum gravitational field can do so. Drawing upon the fundamental relationship between conservation laws and the quantum properties of objects, our analysis offers new perspectives for the study of quantum gravity and provides a novel interpretation of existing experimental observations, such as free fall.

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time T, where the system is governed by a time-dependent Schr\"odinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schr\"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.

We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert Space followed by an imposition of - what effectively amounts to - a superselection rule. We illustrate this procedure with a qubit and apply it to the Mach-Zehnder interferometer. The procedure is somewhat reminiscent of the constrained quantization of the electromagnetic field, where, in order to manifestly comply with relativity, one enlargers the Hilbert Space by quantizing the longitudinal and scalar modes, only to subsequently introduce a constraint to make sure that they are actually not directly observable.

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the computational basis). Our approach is based upon the intuition that noise exponentially damps non-local correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by only keeping track of the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasi-polynomial time, so long as the distribution anti-concentrates. A number of practical implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: for constant noise rates, any quantum circuit for which error mitigation is efficient on most input states, is also classically simulable on most input states.

We study the quantum coherence and its distribution of N-partite GHZ and W states of bosonic fields in the noninertial frames with arbitrary number of acceleration observers. We find that the coherence of both GHZ and W state reduces with accelerations and freezes in the limit of infinite accelerations. The freezing value of coherence depends on the number of accelerated observers. The coherence of N-partite GHZ state is genuinely global and no coherence exists in any subsystems. For the N-partite W state, however, the coherence is essentially bipartite types, and the total coherence is equal to the sum of coherence of all the bipartite subsystems.

We construct Feynman rules for Lindblad master equations in the operator language of quantum optics: a fixed algebra of elementary operator moves and closed-form propagators for perturbation theory about an exactly solvable, in most cases Gaussian, generator. The expansion separates into a kinematic part (the shift algebra on the Wick-ordered eigenoperators O_{mn}=:(c^dagger)^m c^n:, from which the vertex table for a specified interaction is assembled) and a dynamical part that enters only through the resolvent of the unperturbed generator, diagonal and additive for any stable, diagonalizable Gaussian L_0, including thermal and squeezed reservoirs and correlated decay, and equally available for a two-level emitter, driven or undriven. In the driven Kerr cavity the loop expansion is the semiclassical expansion and the series is asymptotic. In a strongly driven two-level atom, dressed lines replace a series of finite radius by one accurate deep into saturation, one line per Mollow component. For Kerr rings and chains the cost is polynomial in the number of sites at fixed perturbative order. On a three-site ring the diagrams recover the non-Gaussian part of the three-photon correlation that the Gaussian cumulant closure lacks; carried to tenth order they give the smallest g^{(3)} error of the methods compared for Uleq0.25κ at a cost below that of a fourth-order closure, and third- and fourth-order closures are more accurate at moderate coupling. The same rules, extended to the counting-field-tilted generator, give the photon-counting cumulants of a disordered eight-site chain beyond direct diagonalization; quantum-jump trajectories at three couplings agree with them to within 1.6 standard errors, within one at the strongest coupling, where they place the third cumulant six standard errors above the Gaussian value.

Weak perturbations of equal size can produce terminal Wasserstein errors of different orders. For Gaussian-smoothed infinitely divisible laws, we differentiate distribution functions with respect to variance-weighted Lévy characteristics, including distributional directions generated by moving atoms. We obtain first- and second-order expansions uniform over Lipschitz tests. Gaussian analyticity identifies the signed second coefficient of the Wasserstein-1 distance when the first response is nonzero. When it vanishes, a finite second displacement moment yields a quadratic response, strictly positive for nonzero displacement dispersion. For local balanced remeshing, the error is comparable to the grid-alignment variance, giving sharp quadratic grid rates for compactly supported densities and nonaligned atomic sequences. We derive metric speed and length along admissible non-atomic curves and a response-based linear program with a certified oracle gap and consistent quadrature. We also establish the sharp vanishing-smoothing transition and a multivariate second-order expansion. The Supplement treats state-dependent responses and further stability estimates.

This work investigates a case study of using physical-based sonification of Quadratic Unconstrained Binary Optimization (QUBO) problems, optimized by the Variational Quantum Eigensolver (VQE) algorithm. The VQE approximates the solution of the problem by using an iterative loop between the quantum computer and a classical optimization routine. This work explores the intermediary statevectors found in each VQE iteration as the means of sonifying the optimization process itself. The implementation was realised in the form of a musical interface prototype named Variational Quantum Harmonizer (VQH), providing potential design strategies for musical applications, focusing on chords, chord progressions, and arpeggios. The VQH can be used both to enhance data visualization or to create artistic pieces. The methodology is also relevant in terms of how an artist would gain intuition towards achieving a desired musical sound by carefully designing QUBO cost functions. Flexible mapping strategies could supply a broad portfolio of sounds for QUBO and quantum-inspired musical compositions, as demonstrated in a case study composition, "Dependent Origination" by Peter Thomas and Paulo Itaborai.

A path-integral approach to quantum acoustics is developed here. In contrast to the commonly utilized particle perspective, this emerging field brings forth a long neglected but essential wave paradigm for lattice vibrations. Within the coherent state picture, we formulate a non-Markovian, stochastic master equation that captures the exact dynamics of any system with coupling linear in the bath coordinates and nonlinear in the system coordinates. We further demonstrate the capability of the presented master equation by applying the corresponding procedure to the eminent Fr\"ohlich model. In general, we establish a solid foundation for quantum acoustics as a kindred framework to quantum optics, while paving the way for deeper first-principle explorations of non-perturbative system dynamics driven by lattice vibrations.

In a class of quantum circuits known as peaked circuits, the goal is to predict the most probable bit string at the output of the circuit. Since these circuits are designed to have a sharp peak in their output distribution, in principle it should be possible to simulate them using a truncated state vector with a limited number of terms, or a fraction of the total probability mass. This approximate simulation can be carried out on a classical computer with a sparse representation that stores only the nonzero amplitudes of the state vector, in contrast to the dense representations that are common in most quantum simulators. For efficiency, all operations on the state vector should be vectorized to the furthest possible extent and, if available, hardware acceleration can also be used. This work describes how these requirements were met in an open-source implementation, and discusses its performance and limitations.

Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing limited quantum computers can contribute to this enhancement. In this work, we explore a new hybrid, efficient quantum-classical representation of quantum states, the multiple-basis representation. This representation consists of a linear combination of states that are sparse in some given and different bases, specified by quantum circuits. Such representation is particularly appealing when considering depth-limited quantum circuits within reach of current hardware. We analyze the expressivity of multiple-basis representation states depending on the classical simulability of their quantum circuits. In particular, we show that multiple-basis representation states include, but are not restricted to, both matrix-product states and stabilizer states. Furthermore, we find cases in which this representation can be used, namely approximation of ground states, simulation of deeper computations by specifying bases with shallow circuits, and a tomographical protocol to describe states as multiple-basis representations. We envision this work to open the path of simultaneous use of several hardware-friendly bases, a natural description of hybrid computational methods accessible for near-term hardware.

This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the star-exponential with the quantum propagator for bosonic systems, this work develops the analogous extension for the fermionic case. A rigorous method, based on Grassmann variables and coherent states, is constructed to obtain a closed-form expression for the fermionic star-exponential from its associated propagator. As a primary application, a fermionic version of the Feynman-Kac formula is derived within this formalism, allowing for the calculation of the ground state energy directly in phase space. Finally, the method is validated by successfully applying it to the simple and driven harmonic oscillators, where it is demonstrated that a simplified ("naive") approach (with an ad-hoc "remediation") is a valid weak-coupling limit of the rigorous ("meticulous") formalism, thereby providing a new and powerful computational tool for the study of fermionic systems.

Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here we provide an experimental demonstration of property estimation based on classical shadows proposed in [H.-Y. Huang, R. Kueng, J. Preskill. Nat. Phys. https://doi.org/10.1038/s41567-020-0932-7 (2020)] and study its performance in the quantum optical experiment with high-dimensional spatial states of photons. We show on experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements.

We review the unconventional photon blockade mechanism. This quantum effect remarkably enables a strongly sub-Poissonian light statistics, even from a system characterized by a weak single photon nonlinearity. We revisit the past results, which can be interpreted in terms of quantum interferences or optimal squeezing, and show how recent developments on input-output field mixing can overcome the limitations of the original schemes towards passive and integrable single photon sources. We finally present some valuable alternative schemes for which the unconventional blockade can be directly adapted.

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short distances; interaction of photons with the graviton background leading to the important cosmological consequences; the time delay of photons due to interactions with gravitons; deceleration of massive bodies in the graviton background which may be connected with the Pioneer anomaly and with the problem of dark matter.

We introduce an open-source package called QTraj that solves the Lindblad equation for heavy-quarkonium dynamics using the quantum trajectories algorithm. The package allows users to simulate the suppression of heavy-quarkonium states using externally-supplied input from 3+1D hydrodynamics simulations. The code uses a split-step pseudo-spectral method for updating the wave-function between jumps, which is implemented using the open-source multi-threaded FFTW3 package. This allows one to have manifestly unitary evolution when using real-valued potentials. In this paper, we provide detailed documentation of QTraj 1.0, installation instructions, and present various tests and benchmarks of the code.

We review the appearance of the Planckian time τ_Pl = hbar/(k_B T) in both conventional and unconventional metals. We give a pedagogical discussion of the various different timescales (quasiparticle, transport, many-body) that characterize metals, emphasizing conditions under which these times are the same or different. Throughout, we have attempted to clear up aspects of the problem that had been confusing us, in the hope that this helps the reader as well. We discuss the possibility of a Planckian bound on dissipation from both a quasiparticle and a many-body perspective. Planckian quasiparticles can arise naturally from a combination of inelastic scattering and mass renormalization. Many-body dynamics, on the other hand, is constrained by the basic time- and length- scales of local thermalization.

Let Msubset B(H) be a semifinite von Neumann algebra, where B(H) denotes the algebra of all bounded linear operators on a Hilbert space H, and let τ be a fixed faithful normal semifinite trace on M.Let E_τ be the fully symmetric space associated with a fully symmetric Banach function space E on [0,infty).Using a complex interpolation argument based on the three-lines theorem on a strip, we show that for positive operators a,bin E_τ and tin[0,1], $ |a^t b^{1-t}+b^t a^{1-t}|_{E_τ}le 2^{max{2|t-1/2|-1/2,;0}};|a+b|_{E_τ}. In particular, we obtain the sharp constant 1 for t\in[1/4,3/4]: |a^t b^{1-t}+b^t a^{1-t}|_{E_τ}le |a+b|_{E_τ}. $ This extends the work of Kittaneh--Ricard in Linear Algebra Appl. 710 (2025), 356--362 and covers the results of Liu--He--Zhao in Acta Math. Sci. Ser. B (Engl. Ed.) 46 (2026), 62--68

Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation" algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while usually only use a constant number of ancilla qubits. We show that singular value transformation leads to novel algorithms. We give an efficient solution to a certain "non-commutative" measurement problem and propose a new method for singular value estimation. We also show how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum. Finally, as a quantum machine learning application we show how to efficiently implement principal component regression. "Singular value transformation" is conceptually simple and efficient, and leads to a unified framework of quantum algorithms incorporating a variety of quantum speed-ups. We illustrate this by showing how it generalizes a number of prominent quantum algorithms, including: optimal Hamiltonian simulation, implementing the Moore-Penrose pseudoinverse with exponential precision, fixed-point amplitude amplification, robust oblivious amplitude amplification, fast QMA amplification, fast quantum OR lemma, certain quantum walk results and several quantum machine learning algorithms. In order to exploit the strengths of the presented method it is useful to know its limitations too, therefore we also prove a lower bound on the efficiency of singular value transformation, which often gives optimal bounds.

Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood as key operational resources for quantum computation, communication, and simulation. Although traditionally investigated in distinct settings, recent theoretical and experimental advances have revealed deep conceptual, mathematical, and operational connections between them. This review presents a unified perspective on these developments based on sheaf-theoretic and graph-theoretic frameworks, which provide theory-independent characterizations of statistical correlations. These approaches clarify the structural relationship between contextuality and nonlocality, facilitate the formulation of experimentally testable inequalities, and guide implementations in realistic physical platforms, with particular emphasis on photonic systems. By bridging abstract theoretical structures and concrete experimental realizations, this review sheds light on the nonclassical foundations of quantum correlations and their emerging role in quantum technologies.

We theoretically identify the noise-induced coherent contribution to the ergotropy of a four-level quantum heat engine coupled to a unimodal quantum cavity. We utilize a protocol where the passive state's quasiprobabilities can be analytically identified from the population-coherence coupled reduced density matrix. The reduced density matrix elements are evaluated using a microscopic quantum master equation formalism. Multiple ergotropies within the same coherence interval, each characterized by a positive and pronounced coherent contribution, are observed. These ergotropies are a result of population inversion as well as quasiprobability-population inversion, controllable through the coherence measure parameters. The optimal flux and power of the engine are found to be at moderate values of ergotropy with increasing values of noise-induced coherence. The optimal power at different coherences is found to possess a constant ergotropy.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

One of the distinguishing aspects of CP2K is its seamless integration of diverse structural and transition-state optimization techniques with advanced sampling approaches including Monte Carlo, molecular dynamics, and metadynamics, enabling the efficient exploration of complex potential- and free-energy landscapes, including rare events. These capabilities are combined with a broad hierarchy of energy and force evaluation methods, ranging from classical and machine-learned interaction potentials and mixed quantum-classical multiscale and semiempirical schemes, to highly accurate quantum-mechanical electronic-structure approaches. At the heart of the latter lies the Gaussian and plane-wave framework, along with its augmented all-electron generalization, which have been described in detail in our previous code review [T. D. Kühne et al., J. Chem. Phys. 152, 194103 (2020)]. Building on this foundation, the present work revisits the methods within CP2K that turn electronic structure into dynamics, transport, and spectroscopic response. Particular emphasis is placed on the coupling between static response calculations and nuclear motion: spectra may be evaluated at optimized structures, averaged over thermally sampled configurations, obtained from time-correlation functions along ab-initio or path integral molecular trajectories, or followed in real time together with electronic and nuclear dynamics. The same modular structure also enables equilibrium and biased transport simulations, from Kubo-type linear response to open-boundary approaches under external potentials, highlighting CP2K's unique capability to unify quantum chemistry with quantum and statistical mechanics within a versatile, holistic simulation environment.

I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schr\"odinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.

The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical complexity theory. This means that we do not know for which calculations there will be a "quantum advantage," once an algorithm is found. One way to answer the question is to find those algorithms, but finding truly quantum algorithms turns out to be very difficult. In previous work over the past three decades we have pursued the idea of using techniques of machine learning to develop algorithms for quantum computing. Here we compare the performance of standard real- and complex-valued classical neural networks with that of one of our models for a quantum neural network, on both classical problems and on an archetypal quantum problem: the computation of an entanglement witness. The quantum network is shown to need far fewer epochs and a much smaller network to achieve comparable or better results.

We point out that the Lyapunov exponent of the eigenstate places restrictions on the eigenvalue. Consequently, with regard to non-Hermitian systems, even without any symmetry, the non-conservative Hamiltonians can exhibit real spectra as long as Lyapunov exponents of eigenstates inhibit imaginary parts of eigenvalues. Our findings open up a new route to study non-Hermitian physics.

Cavity optomechanical systems in the quantum regime consist of a cavity mode and mechanical element coupled together through radiation pressure. In the nonlinear optomechanical regime, open-system dynamics is generally challenging to treat analytically, since the noise terms do not commute with the optomechanical interaction term. Specifically, a general treatment of both Markovian and non-Markovian mechanical noise in the nonlinear optomechanical regime is still outstanding. Here we address this question by solving the full dynamics of an optomechanical system in the nonlinear regime where the mechanical element interacts with a bath of harmonic oscillators, representing full quantum Brownian motion. The solutions, which are exact and analytic, allow us to consider the strength of the optomechanical nonlinearity in the presence of both Markovian (Ohmic) and non-Markovian (sub-Ohmic and super-Ohmic) baths. We show that that while the strength of the nonlinearity is generally reduced by a Markovian bath spectrum, it can be enhanced by constructing a bath with a highly non-Markovian structure. The results have potential implications for future optomechanical experiments which seek to achieve a strong optomechanical nonlinearity.

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

In recent years, there has been tremendous progress in the development of quantum computing hardware, algorithms and services leading to the expectation that in the near future quantum computers will be capable of performing simulations for natural science applications, operations research, and machine learning at scales mostly inaccessible to classical computers. Whereas the impact of quantum computing has already started to be recognized in fields such as cryptanalysis, natural science simulations, and optimization among others, very little is known about the full potential of quantum computing simulations and machine learning in the realm of healthcare and life science (HCLS). Herein, we discuss the transformational changes we expect from the use of quantum computation for HCLS research, more specifically in the field of cell-centric therapeutics. Moreover, we identify and elaborate open problems in cell engineering, tissue modeling, perturbation modeling, and bio-topology while discussing candidate quantum algorithms for research on these topics and their potential advantages over classical computational approaches.

In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a one-particle problem in very high dimension to which we apply different theoretical methods tailored for high-dimensional lattices: the Forward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and the cavity method. Our results indicate the existence of two transition lines and three distinct dynamical phases: a completely many-body localized phase at low energy, a fully ergodic phase at high energy, and a multifractal "bad metal" phase at intermediate energy. In the latter, eigenfunctions occupy a diverging volume, yet an exponentially vanishing fraction of the total Hilbert space. We discuss the limitations of our approximations and the relationship with previous studies.

We present a non-perturbative framework for the quantum treatment of vibrational excitation in molecular systems driven by electric fields with arbitrary time dependence. For harmonic potentials with linear dipole coupling, the field-induced dynamics is exactly described by a displaced coherent state, whose evolution is completely determined by a complex phase-space coordinate. Closed-form expressions for this coordinate reveal a clear distinction between resonant and non-resonant regimes. The resulting vibrational populations follow a Poisson distribution determined by a dimensionless time-dependent phase-space displacement, for both resonant and non-resonant driving. Resonant driving results in an enhanced phase-space displacement, whereas finite detuning between the driving and vibrational frequencies leads to an exponential suppression of the phase-space displacement and vibrational excitation. While the approach reduces to the standard time-dependent perturbation theory in the weak-field limit, it remains valid in the strong-field regime, where perturbative treatments fail. Our results provide a transparent phase-space picture of vibrational control and enable non-perturbative state preparation in ultrafast spectroscopy.

In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon [arXiv:1711.07945]. Equations are presented using a diagrammatic calculus for tensor categories. To this quantum question and answer setting, we extend the standard definitions, including strategies, correlations, and synchronicity, and we use these definitions to extend results about synchronicity. We extend the graph homomorphism (isomorphism) game to quantum graphs, and show it is synchronous (bisynchronous) and connect its perfect (bi)strategies to quantum graph homomorphisms (isomorphisms). Our extended definitions agree with the existing quantum games literature, except in the case of synchronicity.

Tellegen medium has long been a topic of debate, with its existence being contested over several decades. It was first proposed by Tellegen in 1948 and is characterized by a real-valued cross coupling between electric and magnetic responses, distinguishing it from the well-known chiral medium that has imaginary coupling coefficients. Significantly, Tellegen responses are closely linked to axion dynamics, an extensively studied subject in condensed matter physics. Here, we report the realization of Tellegen metamaterials in the microwave region through a judicious combination of subwavelength metallic resonators, gyromagnetic materials, and permanent magnet discs. We observe the key signature of the Tellegen response, i.e. a Kerr rotation for reflected wave, while the polarization remains the same in the transmission direction. The retrieved effective Tellegen parameter is several orders of magnitude greater than that of natural materials. Our work opens door to a variety of nonreciprocal photonic devices and may provide a platform for studying axion physics.

We present a rigorous analysis of the algebraic and geometric structure of the quantum complexity resource of a system of bosonic modes in Gaussian boson sampling. This resource underlies the quantum advantage of the system: its photon-counting statistics require the evaluation of a hafnian of the resource covariance matrix, and that computation is #P-hard. The resource covariance matrix is the solution of a semidefinite program that extracts the minimum-trace physical quantum part of the total covariance matrix; the complementary part is positive semidefinite and can therefore be simulated classically. Earlier work characterized this resource only through the trace of the quantum part, equal to its photon number. We characterize the optimizer itself, as a quantum state and as a geometric object, beyond the scalar given by its trace. We prove that it is a unique pure Gaussian state and construct an explicit oracle map, obeying an algebraic Riccati identity, that reconstructs the resource. We prove that the full problem compresses exactly onto the active symplectic sector that the dual program support generates. The passive-diagonalizable states are solved in closed form, the first explicit solvable class, and the whole program is shown to be equivalent to a minimization over the symplectic group, that is, over the Siegel upper half-space. Together these results establish that the program determines a canonical localized pure Gaussian component of the resource, and they provide the structural foundation for its detailed analysis.

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on Nv , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64*64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers.

This paper addresses the problem of averaged controllability for the time-fractional Schrodinger equation, where the quantum diffusivity parameter is a random variable with a general probability distribution. First, by exploiting the analyticity of the Mittag-Leffler function and Muntz's theorem, we show that the simultaneous null controllability of the system can occur only for a countable set of realizations of the random diffusivity. In particular, this implies the impossibility of simultaneous null controllability for absolutely continuous random diffusivity. Next, we prove the lack of exact averaged controllability for absolutely continuous random variables, irrespective of the control time. Furthermore, we introduce a new two-parameter fractional characteristic function, which allows us to construct a class of random variables satisfying null averaged controllability at any time from any arbitrary sensor set of positive Lebesgue measure. This is achieved using an open-loop control belonging to L^\infty and independent of the random parameter. In particular, we obtain the null controllability of the fractional biharmonic diffusion equation. Finally, we conclude with several remarks and open problems that merit future investigation.

Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its role in the dynamics of systems and hinders any formulation to merge quantum mechanics with general relativity, specifically when considering quantum gravity. To overcome those limitations, several authors tried to construct an operator which is conjugate to the Hamiltonian of quantum systems implementing some essential features of the relativistic time. These formulations use the concept of internal or intrinsic time instead of the universal coordinate time used in textbooks. Furthermore, recently it is remarked that the consideration of time with relativistic features could enhance the analysis techniques in quantum information processing and have an impact on its status in causal orders and causal structures of quantum information. The role of clocks, their accuracy and stability has become an important issue in quantum information processing. This article present a substantiative review of recent works which reflect the possibility of utilizing quantum time, measured by quantum clock devised according to Page-Wootters scheme, to stand as a resource for quantum information processing.

In this work, we describe strategies and provide case-study activities that can be used to examine the properties of superposition, entanglement, tagging, complementarity, and measurement in quantum curricula geared for teacher training. Having a solid foundation in these conceptual ideas is critical for educators who will be adopting quantum ideas within the classroom. Yet they are some of the most difficult concepts to master. We show how one can systematically develop these conceptual foundations with thought experiments on light and with thought experiments that employ the Stern-Gerlach experiment. We emphasize the importance of computer animations in aiding the instruction on these concepts.

A cylindrical TM_{0,1,0} mode microwave cavity resonator was excited using a balanced interferometric configuration that allowed manipulation of the electric field and potential within the resonator by adjusting the phase and amplitude of the interferometer arms driving the resonator. With precise tuning of the phase and amplitude, 25 dB suppression of the electric field at the resonance frequency was achieved while simultaneously resonantly enhancing the time-varying electric-scalar potential. Under these conditions, the system demonstrated electromagnetically induced absorption in the cavity response due to the annulment of the electric field at the resonance frequency. This phenomena can be regarded as a form of extreme dispersion, and led to a sharp increase in the cavity phase versus frequency response by an order of magnitude when compared to the cavity Q-factor. This work presents an experimental setup that will allow the electric-scalar Aharonov-Bohm effect to be tested under conditions involving a time-varying electric-scalar potential, without the presence of an electric field or magnetic vector potential, an experiment that has not yet been realised.

Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We validate these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP=BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.

Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and processes that data using a quantum computer, could have significant advantages over conventional experiments in which the physical system is measured and the outcomes are processed using a classical computer. We prove that, in various tasks, quantum machines can learn from exponentially fewer experiments than those required in conventional experiments. The exponential advantage holds in predicting properties of physical systems, performing quantum principal component analysis on noisy states, and learning approximate models of physical dynamics. In some tasks, the quantum processing needed to achieve the exponential advantage can be modest; for example, one can simultaneously learn about many noncommuting observables by processing only two copies of the system. Conducting experiments with up to 40 superconducting qubits and 1300 quantum gates, we demonstrate that a substantial quantum advantage can be realized using today's relatively noisy quantum processors. Our results highlight how quantum technology can enable powerful new strategies to learn about nature.

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the Generalized Gibbs Ensemble description for this infinite dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve towards the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a Generalized Gibbs Ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states which would potentially not be described by the Gibbs Generalized Ensemble description.

From the dynamics of a broad class of classical mean-field glass models one may obtain a quantum model with finite zero-temperature entropy, a quantum transition at zero temperature, and a time-reparametrization (quasi-)invariance in the dynamical equations for correlations. The low eigenvalue spectrum of the resulting quantum model is directly related to the structure and exploration of metastable states in the landscape of the original classical glass model. This mapping reveals deep connections between classical glasses and the properties of SYK-like models.

We propose a quantum version of a generative diffusion model. In this algorithm, artificial neural networks are replaced with parameterized quantum circuits, in order to directly generate quantum states. We present both a full quantum and a latent quantum version of the algorithm; we also present a conditioned version of these models. The models' performances have been evaluated using quantitative metrics complemented by qualitative assessments. An implementation of a simplified version of the algorithm has been executed on real NISQ quantum hardware.

Recently, Fernandes discovered an analytic solution for rotating black holes in semiclassical gravity induced by the trace anomaly. These solutions exhibit some distinctive characteristics, including a non-spherically symmetric event horizon and violations of the Kerr bound. As a crucial assumption to uphold causality in spacetime, we investigate the validity of the weak cosmic censorship conjecture (WCCC) within this class of solutions with type-A trace anomaly by introducing a test particle on the equatorial plane. Our study reveals three distinct mechanisms that can potentially destroy the event horizon, leading to a violation of the WCCC. Our findings indicate that, with the exception of extremal Kerr, static extremal, and static singular black holes, the WCCC may be violated under the first-order perturbation of the test particle. These results suggest the need for further exploration of modifications to the behavior of the test particle under quantum effects in order to address the violation of the WCCC in this system.

Reservoir computing (RC) is among the most promising approaches for AI-based prediction models of complex systems. It combines superior prediction performance with very low CPU-needs for training. Recent results demonstrated that quantum systems are also well-suited as reservoirs in RC. Due to the exponential growth of the Hilbert space dimension obtained by increasing the number of quantum elements small quantum systems are already sufficient for time series prediction. Here, we demonstrate that three-dimensional systems can already well be predicted by quantum reservoir computing with a quantum reservoir consisting of the minimal number of qubits necessary for this task, namely four. This is achieved by optimizing the encoding of the data, using spatial and temporal multiplexing and recently developed read-out-schemes that also involve higher exponents of the reservoir response. We outline, test and validate our approach using eight prototypical three-dimensional chaotic systems. Both, the short-term prediction and the reproduction of the long-term system behavior (the system's "climate") are feasible with the same setup of optimized hyperparameters. Our results may be a further step towards the realization of a dedicated small quantum computer for prediction tasks in the NISQ-era.

Excited electronic states are difficult to accurately and tractably model, particularly those exhibiting multiexcitonic character. Scalable single-reference excited state methods typically fail to describe such states as they suffer from the defects of the mean-field approximation and/or neglect higher-rank excitation operators. To address this, we derive the [T] perturbative correction to the quantum self-consistent equation-of-motion unitary coupled cluster singles and doubles (q-sc-EOM-UCCSD) method. The method captures triple excitation effects through a classical step of second-order in many-body perturbation theory following a q-sc-EOM-UCCSD calculation on a quantum computer. The perturbative correction developed has a O(N^7) classical computational time scaling. We incorporate [T] into a hybrid compute strategy wherein eigenvectors of the effective Hamiltonian from the hybrid quantum-classical q-sc-EOM-UCCSD algorithm are relayed to a classical computer which performs the postprocessing required for the [T] correction. The benefits of [T] are quantified in a benchmark covering a variety of electronically excited states of the isoelectronic CH^+ and BH molecules. We find that the addition of the [T] correction to both trotterized and full operator variants of q-sc-EOM-CCSD can offer dramatic improvements over baseline q-sc-EOM-UCCSD. Our assessment clearly demonstrates the importance of considering higher-rank excitation operators in q-sc-EOM-UCCSD, quantifies the overall success of the [T] correction, and discusses some of its limitations.

We study complex saddle points of the worldline path integral for massive charged particles in two-dimensional maximally symmetric backgrounds threaded by homogeneous electric fields. Within the worldline formalism, we show that the semiclassical saddles generically require complexifying both the target spacetime and the proper-time parameter. The resulting solutions comprise two slices of a single complex family, distinguished by the direction of proper-time evolution. The one evolving in imaginary proper time carries an action that typically controls the exponential suppression of non-perturbative effects, while that evolving in real proper time may encode additional complex phases responsible for quantum interference between saddles. Treating this family as a whole, we give a prescription for constructing and classifying all topologically inequivalent instanton sectors, and we find that the worldline action depends only on their topological data, namely winding numbers around the compact directions and certain isolated punctures. Moreover, in Anti-de Sitter spacetime, the qualitative structure of the solutions is governed by the dimensionless ratio R |eE|/m (R being the curvature radius), which distinguishes sub-extremal, extremal, and super-extremal regimes. By contrast, no analogous distinction occurs in de Sitter---where the instantons are insensitive to this ratio---or in Minkowski spacetime, which lacks a curvature scale altogether. We also recast the action as a sum over residues of the relevant (non-conserved) conjugate momentum, making transparent which analytic data control each contribution. Finally, we discuss the subtleties that arise when solutions built in various local patches are lifted to global (Anti-)de Sitter space. These impose further necessary conditions on which saddles can in principle contribute to the one-loop path integral.

Feynman famously asserted that interference is the only real mystery in quantum mechanics (QM). It is concluded that the reason for this mystery, and thereby the related mysteries of complementarity, non-commutativity of observables, the uncertainty principle and violation of Bell's equality, is that the axioms of QM depend vitally on the continuum nature of Hilbert Space, deemed unphysical. We develop a theory of quantum physics - Rational Quantum Mechanics (RaQM) - in which Hilbert Space is gravitationally discretised. The key to solving the mysteries of QM in RaQM is a number-theoretic property of the cosine function, concealed in QM when angles range over the continuum. This number-theoretic property describes mathematically the utter indivisibility of the quantum world and implies that the laws of physics are profoundly holistic. We contrast holism with nonlocality. In theories which embrace the continuum, the violation of Bell's inequality requires the laws of physics to be either nonlocal or not realistic; both incomprehensible concepts. By contrast, holism, as embodied in Mach's Principle or in the fractal geometry of a chaotic attractor, is neither incomprehensible nor unphysical. As part of this, we solve the deepest mystery of all; why nature makes use of complex numbers.

Regression is a cornerstone of statistics and machine learning, with applications spanning science, engineering, and economics. While quantum algorithms for regression have attracted considerable attention, most existing work has focused on linear regression, leaving many more complex yet practically important variants unexplored. In this work, we present a unified quantum framework for accelerating a broad class of regression tasks -- including linear and multiple regression, Lasso, Ridge, Huber, ell_p-, and δ_p-type regressions -- achieving up to a quadratic improvement in the number of samples m over the best classical algorithms. This speedup is achieved by extending the recent classical breakthrough of Jambulapati et al. (STOC'24) using several quantum techniques, including quantum leverage score approximation (Apers &Gribling, 2024) and the preparation of many copies of a quantum state (Hamoudi, 2022). For problems of dimension n, sparsity r < n, and error parameter ε, our algorithm solves the problem in O(rmn/ε+ poly(n,1/ε)) quantum time, demonstrating both the applicability and the efficiency of quantum computing in accelerating regression tasks.

Benchmarking models via classical simulations is one of the main ways to judge ideas in quantum machine learning before noise-free hardware is available. However, the huge impact of the experimental design on the results, the small scales within reach today, as well as narratives influenced by the commercialisation of quantum technologies make it difficult to gain robust insights. To facilitate better decision-making we develop an open-source package based on the PennyLane software framework and use it to conduct a large-scale study that systematically tests 12 popular quantum machine learning models on 6 binary classification tasks used to create 160 individual datasets. We find that overall, out-of-the-box classical machine learning models outperform the quantum classifiers. Moreover, removing entanglement from a quantum model often results in as good or better performance, suggesting that "quantumness" may not be the crucial ingredient for the small learning tasks considered here. Our benchmarks also unlock investigations beyond simplistic leaderboard comparisons, and we identify five important questions for quantum model design that follow from our results.

This review presents recent breakthroughs in the realm of nonlinear Hall effects, emphasizing central theoretical foundations and recent experimental progress. We elucidate the quantum origin of the second-order Hall response, focusing on the Berry curvature dipole, which may arise in inversion symmetry broken systems. The theoretical framework also reveals the impact of disorder scattering effects on the nonlinear response. We further discuss the possibility of obtaining nonlinear Hall responses beyond the second order. We examine symmetry-based indicators essential for the manifestation of nonlinear Hall effects in time-reversal symmetric crystals, setting the stage for a detailed exploration of theoretical models and candidate materials predicted to exhibit sizable and tunable Berry curvature dipole. We summarize groundbreaking experimental reports on measuring both intrinsic and extrinsic nonlinear Hall effects across diverse material classes. Finally, we highlight some of the other intriguing nonlinear effects, including nonlinear planar Hall, nonlinear anomalous Hall, and nonlinear spin and valley Hall effects. We conclude with an outlook on pivotal open questions and challenges, marking the trajectory of this rapidly evolving field.

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

Quantum computation is an emerging technology with important potential for solving certain problems pivotal in various scientific and engineering disciplines. This paper introduces an efficient quantum protocol for the explicit construction of the block-encoding for an important class of Hamiltonians. Using the Schrodingerisation technique -- which converts non-conservative PDEs into conservative ones -- this particular class of Hamiltonians is shown to be sufficient for simulating any linear partial differential equations that have coefficients which are polynomial functions. The class of Hamiltonians consist of discretisations of polynomial products and sums of position and momentum operators. This construction is explicit and leverages minimal one- and two-qubit operations. The explicit construction of this block-encoding forms a fundamental building block for constructing the unitary evolution operator for this Hamiltonian. The proposed algorithm exhibits polynomial scaling with respect to the spatial partitioning size, suggesting an exponential speedup over classical finite-difference methods. This work provides an important foundation for building explicit and efficient quantum circuits for solving partial differential equations.

We study sampling algorithms for β-ensembles with time complexity less than cubic in the cardinality of the ensemble. Following Dumitriu & Edelman (2002), we see the ensemble as the eigenvalues of a random tridiagonal matrix, namely a random Jacobi matrix. First, we provide a unifying and elementary treatment of the tridiagonal models associated to the three classical Hermite, Laguerre and Jacobi ensembles. For this purpose, we use simple changes of variables between successive reparametrizations of the coefficients defining the tridiagonal matrix. Second, we derive an approximate sampler for the simulation of β-ensembles, and illustrate how fast it can be for polynomial potentials. This method combines a Gibbs sampler on Jacobi matrices and the diagonalization of these matrices. In practice, even for large ensembles, only a few Gibbs passes suffice for the marginal distribution of the eigenvalues to fit the expected theoretical distribution. When the conditionals in the Gibbs sampler can be simulated exactly, the same fast empirical convergence is observed for the fluctuations of the largest eigenvalue. Our experimental results support a conjecture by Krishnapur et al. (2016), that the Gibbs chain on Jacobi matrices of size N mixes in O(log(N)).

Harnessing integrability at arbitrary interaction strength, we build long-lived and spatially localized soliton-like excitations in the 1D Bose gas with contact repulsion (Lieb-Liniger model). We show how these density profiles, built from selective superpositions of multi-hole eigenstates, display long lifetimes tunable through parameters like dispersion width and number of holes. We further illustrate a scaling protocol that in principle enables unbounded increase in lifetimes in the thermodynamic limit. Our results showcase classical-like excitations originating from unitary quantum dynamics, away from the semi-classical regime, and in regions where interactions cannot be treated perturbatively.

We introduce a new predator-prey model by replacing the growth and predation constant by a square matrix, and the population density as a population vector. The classical Lotka-Volterra model describes a population that either modulates or converges. Stability analysis of such models have been extensively studied by the works of Merdan (https://doi.org/10.1016/j.chaos.2007.06.062). The new model adds complexity by introducing an age group structure where the population of each age group evolves as prescribed by the Leslie matrix. The added complexity changes the behavior of the model such that the population either displays roughly an exponential growth or decay. We first provide an exact equation that describes a time evolution and use analytic techniques to obtain an approximate growth factor. We also discuss the variants of the Leslie model, i.e., the complex value predator-prey model and the competitive model. We then prove the Last Species Standing theorem that determines the dominant population in the large time limit. The recursive structure of the model denies the application of simple regression. We discuss a machine learning scheme that allows an admissible fit for the population evolution of Paramecium Aurelia and Paramecium Caudatum. Another potential avenue to simplify the computation is to use the machinery of quantum operators. We demonstrate the potential of this approach by computing the Hamiltonian of a simple Leslie system.

In this paper we prove, both mathematically and through a simulation, how the Quantum Amplitude Estimation algorithm can obtain quadratic improvements with respect to the Monte Carlo method in gradient-based stochastic optimization, highlighting the central role of the Quantum Phase Estimation concentration guarantee in achieving the predicted advantage.

High-accuracy microwave sensing is widely demanded in various fields, ranging from cosmology to microwave quantum technology. Quantum receivers based on inorganic solid-state spin systems are promising candidates for such purpose because of the stability and compatibility, but their best sensitivity is currently limited to a few pT/rm{Hz}. Here, by utilising an enhanced readout scheme with the state-of-the-art solid-state maser technology, we develop a robust microwave quantum receiver functioned by organic molecular spins at ambient conditions. Owing to the maser amplification, the sensitivity of the receiver achieves 6.14 pm 0.17 fT/rm{Hz} which exceeds three orders of magnitude than that of the inorganic solid-state quantum receivers. The heterodyne detection without additional local oscillators improves bandwidth of the receiver and allows frequency detection. The scheme can be extended to other solid-state spin systems without complicated control pulses and thus enables practical applications such as electron spin resonance spectroscopy, dark matter searches, and astronomical observations.

Reciprocity is a fundamental symmetry present in many natural phenomena and engineered systems. Distinct situations where this symmetry is broken are typically grouped under the umbrella term "nonreciprocity", colloquially defined by: the action of A on B neq the action of B on A. In this review, we elucidate what nonreciprocity is by providing an introduction to its most salient classes: nonvariational dynamics, violations of Newton's third law, broken detailed balance, nonreciprocal responses and nonreciprocity of arbitrary linear operators. Next, we point out where to find these manifestations of non-reciprocity, from ensembles of particles with field mediated interactions to synthetic neural networks and open quantum systems. Given this breadth of contexts and the lack of an all-encompassing definition, it makes it all the more intriguing that some general conclusions can be gathered, when distinct definitions of nonreciprocity overlap. We explore what these universal consequences are with a special emphasis on collective phenomena that arise in nonreciprocal many-body systems. The topics covered include nonreciprocal phase transitions and non-normal amplification of noise and perturbations. We conclude with some open questions.

Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a classical shadow, can be used to predict many different properties: order log M measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size, and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.

This paper focuses on the construction of a general parametric model that can be implemented executing multiple swap tests over few qubits and applying a suitable measurement protocol. The model turns out to be equivalent to a two-layer feedforward neural network which can be realized combining small quantum modules. The advantages and the perspectives of the proposed quantum method are discussed.

This work endeavors to juxtapose the efficacy of machine learning algorithms within classical and quantum computational paradigms. Particularly, by emphasizing on Support Vector Machines (SVM), we scrutinize the classification prowess of classical SVM and Quantum Support Vector Machines (QSVM) operational on quantum hardware over the Iris dataset. The methodology embraced encapsulates an extensive array of experiments orchestrated through the Qiskit library, alongside hyperparameter optimization. The findings unveil that in particular scenarios, QSVMs extend a level of accuracy that can vie with classical SVMs, albeit the execution times are presently protracted. Moreover, we underscore that augmenting quantum computational capacity and the magnitude of parallelism can markedly ameliorate the performance of quantum machine learning algorithms. This inquiry furnishes invaluable insights regarding the extant scenario and future potentiality of machine learning applications in the quantum epoch. Colab: https://t.ly/QKuz0

In this paper, we discuss that an observable-based single-system Copenhagen and entanglement-based two-system von Neumann measurement protocols in quantum theory can be made equivalent by considering the second part of the two-system scheme to be a Dirac-type negative sea filling up the first system. Based on this equivalence, and by considering the universe as a computational process, the choice of the apparatus state in the two-system protocol can be identified with the choice of the observable in the single-system scheme as negative sea filling up the observable universe. In particular, the measuring party's state is considered to be evolving backwards in time to the big bang as a nondeterministic computational process, which chooses the acceptable path as a time-reversal process of irreversible computation. The suggested model proposes that the prepared microstate of the universe, or reality, corresponds to the observer's choice, therefore, subjective reality. Thus, this effectively provides a specific description of the subjective universe model previously proposed, which is based on the symmetry breakdown between the Schrodinger and the Heisenberg pictures of quantum theory.

In October 2007, a Research Proposal for the University of Sydney, Australia, the author suggested that biovie-physical phenomenon as `electrodynamic dependant biological vision', is governed by relativistic quantum laws and biovision. The phenomenon on the basis of `biovielectroluminescence', satisfies man/microbio/megabio/computer vision (MMMCV), as a robust candidate for physical and visual sciences. The general aim of this addendum is to present a refined text of Sections 1-3 of that proposal and highlighting the contents of its Appendix in form of a `Mechanisms' Section. We then briefly remind in an article aimed for December 2007, by appending two more equations into Section 3, a theoretical II-time scenario as a time model well-proposed for the phenomenon. The time model within the core of the proposal, plays a significant role in emphasizing the principle points on Objectives no. 1-8, Sub-hypothesis 3.1.2, mentioned in Article [arXiv:0710.0410]. It also expresses the time concept in terms of causing quantized energy f(|E|) of time |t|, emit in regard to shortening the probability of particle loci as predictable patterns of particle's un-occurred motion, a solution to Heisenberg's uncertainty principle (HUP) into a simplistic manner. We conclude that, practical frames via a time algorithm to this model, fixates such predictable patterns of motion of scenery bodies onto recordable observation points of a MMMCV system. It even suppresses/predicts superposition phenomena coming from a human subject and/or other bio-subjects for any decision making event, e.g., brainwave quantum patterns based on vision. Maintaining the existential probability of Riemann surfaces of II-time scenarios in the context of biovielectroluminescence, makes motion-prediction a possibility.

We provide conceptual and mathematical foundations for near-term quantum natural language processing (QNLP), and do so in quantum computer scientist friendly terms. We opted for an expository presentation style, and provide references for supporting empirical evidence and formal statements concerning mathematical generality. We recall how the quantum model for natural language that we employ canonically combines linguistic meanings with rich linguistic structure, most notably grammar. In particular, the fact that it takes a quantum-like model to combine meaning and structure, establishes QNLP as quantum-native, on par with simulation of quantum systems. Moreover, the now leading Noisy Intermediate-Scale Quantum (NISQ) paradigm for encoding classical data on quantum hardware, variational quantum circuits, makes NISQ exceptionally QNLP-friendly: linguistic structure can be encoded as a free lunch, in contrast to the apparently exponentially expensive classical encoding of grammar. Quantum speed-up for QNLP tasks has already been established in previous work with Will Zeng. Here we provide a broader range of tasks which all enjoy the same advantage. Diagrammatic reasoning is at the heart of QNLP. Firstly, the quantum model interprets language as quantum processes via the diagrammatic formalism of categorical quantum mechanics. Secondly, these diagrams are via ZX-calculus translated into quantum circuits. Parameterisations of meanings then become the circuit variables to be learned. Our encoding of linguistic structure within quantum circuits also embodies a novel approach for establishing word-meanings that goes beyond the current standards in mainstream AI, by placing linguistic structure at the heart of Wittgenstein's meaning-is-context.

This work describes the theoretical foundation for all quantum chemistry functionality in PennyLane, a quantum computing software library specializing in quantum differentiable programming. We provide an overview of fundamental concepts in quantum chemistry, including the basic principles of the Hartree-Fock method. A flagship feature in PennyLane is the differentiable Hartree-Fock solver, allowing users to compute exact gradients of molecular Hamiltonians with respect to nuclear coordinates and basis set parameters. PennyLane provides specialized operations for quantum chemistry, including excitation gates as Givens rotations and templates for quantum chemistry circuits. Moreover, built-in simulators exploit sparse matrix techniques for representing molecular Hamiltonians that lead to fast simulation for quantum chemistry applications. In combination with PennyLane's existing methods for constructing, optimizing, and executing circuits, these methods allow users to implement a wide range of quantum algorithms for quantum chemistry. We discuss how PennyLane can be used to implement variational algorithms for calculating ground-state energies, excited-state energies, and energy derivatives, all of which can be differentiated with respect to both circuit and Hamiltonian parameters. We provide an example workflow describing how to jointly optimize circuit parameters, nuclear coordinates, and basis set parameters for quantum chemistry algorithms. We discuss a functionality for reducing the number of qubits by using symmetries and explain how PennyLane can be used to estimate quantum resources needed to implement several quantum algorithms. By combining insights from quantum computing, computational chemistry, and machine learning, PennyLane is the first library for differentiable quantum computational chemistry.

It has been suggested previously that an ultra-soft fermionic excitation develops, albeit with a small spectral weight, in a system of massless fermions and scalar bosons with Yukawa interaction at high temperature (T). In this paper we study how this excitation is modified at finite chemical potential (μ). We relate the existence of the ultra-soft mode to symmetries, in particular charge conjugation, and a supersymmetry of the free system which is spontaneously broken by finite temperature and finite density effects, as argued earlier by Lebedev and Smilga. A non vanishing chemical potential breaks both symmetries explicitly, and maximally at zero temperature where the mode ceases to exist. A detailed calculation indicates that the ultra-soft excitation persists as long as Tgtrsim μ.

This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing statistical independencies, mediated by Markov blankets, speak to a recursive composition of ensembles (of things) at increasingly higher spatiotemporal scales. This decomposition provides a description of small things; e.g., quantum mechanics - via the Schrodinger equation, ensembles of small things - via statistical mechanics and related fluctuation theorems, through to big things - via classical mechanics. These descriptions are complemented with a Bayesian mechanics for autonomous or active things. Although this work provides a formulation of every thing, its main contribution is to examine the implications of Markov blankets for self-organisation to nonequilibrium steady-state. In brief, we recover an information geometry and accompanying free energy principle that allows one to interpret the internal states of something as representing or making inferences about its external states. The ensuing Bayesian mechanics is compatible with quantum, statistical and classical mechanics and may offer a formal description of lifelike particles.

We discuss the notion of coherent states from three different perspectives: the seminal approach of Schroedinger, the experimental take of quantum optics, and the theoretical developments in quantum gravity. This comparative study tries to emphasise the connections between the approaches, and to offer a coherent short story of the field, so to speak. It may be useful for pedagogical purposes, as well as for specialists of quantum optics and quantum gravity willing to embed their perspective within a wider landscape.

We show that the Hong-Ou-Mandel effect from quantum optics is equivalent to the SWAP test, a quantum information primitive which compares two arbitrary states. We first derive a destructive SWAP test that doesn't need the ancillary qubit that appears in the usual quantum circuit. Then, we study the Hong-Ou-Mandel effect for two photons meeting at a beam splitter and prove it is, in fact, an optical implementation of the destructive SWAP test. This result offers both an interesting simple realization of a powerful quantum information primitive and an alternative way to understand and analyse the Hong-Ou-Mandel effect.

We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

We study the electron-positron to muon--anti-muon cross-section in the asymptotically safe Standard Model. In particular, we include the graviton contributions to the scattering amplitude, which is computed from momentum-dependent time-like one-particle-irreducible correlation functions. Specifically, we employ reconstruction techniques for the graviton spectral functions. We find that the full asymptotically safe quantum cross section decreases in the ultraviolet with the centre-of-mass energy, and is compatible with unitarity bounds. Importantly, our findings provide non-trivial evidence for the unitarity of the asymptotically safe Standard Model.

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr\"{o}dinger equation. In contrast to the standard iterative first order optimization and the time-dependent variational principle, our approach utilizes the implicit mid-point method and generates the solution for all spatial and temporal values simultaneously after optimization. We demonstrate the method in the Schr\"{o}dinger equation with a self-normalized autoregressive spacetime neural network construction. Future explorations for solving different high dimensional differential equations are discussed.

We derive bounds on the lifetime of an evaporating black hole. The bound follows from energy conservation and purification, within the framework of `asymptotically semiclassical spacetimes'. We use the recently derived expression for the Bondi flux of Hawking radiation, together with the expression for the entanglement entropy of Hawking radiation at null infinity, to investigate the purification phase after the last semiclassical ray. We discuss the energy-cost of entanglement purification and we find a lower bound on the purification time of the black hole, which scales as M_0^4/hbar^{3/2}, where M_0 is the initial black hole mass. Additionally, motivated by quantum gravity considerations, we include the additional assumption that a Planck mass black hole is metastable. With this assumption, we find that the the purification time is extended to be exponential in the square of the initial black hole mass, i.e. in its initial area. We find that the redshift exponent is negative in this purification phase, which indicates the existence of a white-hole remnant which releases information slowly. We comment on phenomenological implications for primordial black hole remnants.

We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private numbers, even if using an uncharacterised quantum device potentially built by an adversary. Our generation rates are linear in the repetition rate of the quantum device and the classical randomness post-processing has quasi-linear complexity - making it efficient on a standard personal laptop. The statistical analysis is also tailored for real-world quantum devices. Our protocol is then showcased on several different quantum computers. Although not purposely built for the task, we show that quantum computers can run faithful Bell tests by adding minimal assumptions. In this semi-device-independent manner, our protocol generates (near-)perfectly unbiased and private random numbers on today's quantum computers.

We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts on an input quantum state. For binary classification a single Pauli operator is measured on a designated readout qubit. The measured output is the quantum neural network's predictor of the binary label of the input state. First we look at classifying classical data sets which consist of n-bit strings with binary labels. The input quantum state is an n-bit computational basis state corresponding to a sample string. We show how to design a circuit made from two qubit unitaries that can correctly represent the label of any Boolean function of n bits. For certain label functions the circuit is exponentially long. We introduce parameter dependent unitaries that can be adapted by supervised learning of labeled data. We study an example of real world data consisting of downsampled images of handwritten digits each of which has been labeled as one of two distinct digits. We show through classical simulation that parameters can be found that allow the QNN to learn to correctly distinguish the two data sets. We then discuss presenting the data as quantum superpositions of computational basis states corresponding to different label values. Here we show through simulation that learning is possible. We consider using our QNN to learn the label of a general quantum state. By example we show that this can be done. Our work is exploratory and relies on the classical simulation of small quantum systems. The QNN proposed here was designed with near-term quantum processors in mind. Therefore it will be possible to run this QNN on a near term gate model quantum computer where its power can be explored beyond what can be explored with simulation.

It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}Ψprobability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this probability axiom to the complex plane, we first attempt to find a probability density by solving an appropriate conservation equation. The characteristic curves of this conservation equation are found to be the same as the complex paths of particles in the new representation. The boundary condition in this case is that the extended probability density should agree with the quantum probability rule along the real line. For the simple, time-independent, one-dimensional problems worked out here, we find that a conserved probability density can be derived from the velocity field of particles, except in regions where the trajectories were previously suspected to be nonviable. An alternative method to find this probability density in terms of a trajectory integral, which is easier to implement on a computer and useful for single particle solutions, is also presented. Most importantly, we show, by using the complex extension of Schrodinger equation, that the desired conservation equation can be derived from this definition of probability density.

It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-body interactions in a partially filled Landau level, which becomes exact in the limit where the cyclotron energy is large compared to the interaction strength, so one can ignore mixing between Landau levels. This symmetry is explicit in the description of a half-filled Landau level recently introduced by D. T. Son, using Dirac fermions, but it was thought to be absent in the older fermion-Chern- Simons approach, developed by Halperin, Lee, and Read and subsequent authors. We show here, however, that when properly evaluated, the Halperin, Lee, Read (HLR) theory gives results for long-wavelength low-energy physical properties, including the Hall conductance in the presence of impurities and the positions of minima in the magnetoroton spectra for fractional quantized Hall states close to half-filling, that are identical to predictions of the Dirac formulation. In fact, the HLR theory predicts an emergent particle-hole symmetry near half filling, even when the cyclotron energy is finite.

Binary classical information is routinely encoded in the two metastable states of a dynamical system. Since these states may exhibit macroscopic lifetimes, the encoded information inherits a strong protection against bit-flips. A recent qubit - the cat-qubit - is encoded in the manifold of metastable states of a quantum dynamical system, thereby acquiring bit-flip protection. An outstanding challenge is to gain quantum control over such a system without breaking its protection. If this challenge is met, significant shortcuts in hardware overhead are forecast for quantum computing. In this experiment, we implement a cat-qubit with bit-flip times exceeding ten seconds. This is a four order of magnitude improvement over previous cat-qubit implementations, and six orders of magnitude enhancement over the single photon lifetime that compose this dynamical qubit. This was achieved by introducing a quantum tomography protocol that does not break bit-flip protection. We prepare and image quantum superposition states, and measure phase-flip times above 490 nanoseconds. Most importantly, we control the phase of these superpositions while maintaining the bit-flip time above ten seconds. This work demonstrates quantum operations that preserve macroscopic bit-flip times, a necessary step to scale these dynamical qubits into fully protected hardware-efficient architectures.

Recent results in relativistic quantum information and quantum thermodynamics have independently shown that in the quantum regime, a system may fail to thermalise when subject to quantum-controlled application of the same, single thermalisation channel. For example, an accelerating system with fixed proper acceleration is known to thermalise to an acceleration-dependent temperature, known as the Unruh temperature. However, the same system in a superposition of spatially translated trajectories that share the same proper acceleration fails to thermalise. Here, we provide an explanation of these results using the framework of quantum field theory in relativistic noninertial reference frames. We show how a probe that accelerates in a superposition of spatial translations interacts with incommensurate sets of field modes. In special cases where the modes are orthogonal (for example, when the Rindler wedges are translated in a direction orthogonal to the plane of motion), thermalisation does indeed result, corroborating the here provided explanation. We then discuss how this description relates to an information-theoretic approach aimed at studying quantum aspects of temperature through quantum-controlled thermalisations. The present work draws a connection between research in quantum information, relativistic physics, and quantum thermodynamics, in particular showing that relativistic quantum effects can provide a natural realisation of quantum thermodynamical scenarios.

Between 1972 and 1975, Jacob Bekenstein proposed that black holes possess entropy proportional to their horizon area, and Stephen Hawking derived this relationship from semiclassical quantum field theory in curved spacetime, predicting thermal radiation from black holes. These developments established black hole thermodynamics as a formal framework connecting general relativity, quantum mechanics, and statistical physics. However, this synthesis rests on approximations whose validity remains unproven in regimes where quantum gravitational effects become important. This article provides a detailed overview of the historical development from 1972 to 1975 and surveys modern proposals, such as the holographic principle and gravitational path integrals. We highlight persistent theoretical challenges, including the information paradox, the trans-Planckian problem, backreaction effects, and the absence of experimental verification. The work concludes by identifying which aspects of black hole thermodynamics are well-established and which remain speculative or fundamentally incomplete.

We study the dynamics of gravitons in a squeezed vacuum state in a thermal radiation background. Unlike traditional treatments that rely on the Boltzmann equation, we employ the Heisenberg equation and average it over general quantum states. In contrast to the usual Boltzmann-based descriptions, our approach captures the subtleties arising from quantum coherence in different number eigenstates, which is essential for soft graviton modes in the squeezed vacuum state. Our new method successfully reproduces the previous one-loop results within the in-in formalism when the expansion parameter is small and deviates significantly as the parameter increases, indicating that our results extend beyond the one-loop in-in formalism. We examine the implications of graviton emission effects stimulated by quantum coherence in both flat and expanding backgrounds. In the flat background, it is found that backreaction of radiation on the spacetime dynamics is crucial for significant stimulated emission. In the expanding background, to avoid the subtleties associated with superhorizon modes, we investigate the effect of emission within the horizon immediately after reheating and find a significant effect. We examined the IR graviton evolution from a symmetry perspective and propose a regularization prescription to eliminate the secular growth problem.

We propose a simple modification of space-based gravitational wave (GW) detector optical benches which would enable the measurement of vacuum birefringence of light induced by axion dark matterthrough its coupling to electromagnetism. Specifically, we propose to change a half-wave plate by a circular polarizer. While marginally affecting the sensitivity to GW by a factor 2, we show that such an adjustment would make future detectors such as LISA, TianQin, Taiji and Big-Bang Observer the most sensitive experiments at low axion masses

Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.