Yu. Dabaghian, R. Blümel
We show that all scaling quantum graphs are explicitly integrable, i.e. any one of their spectral eigenvalues $E_n$ is computable analytically, explicitly, and individually for any given $n$. This is surprising, since quantum graphs are excellent models of quantum chaos [see, e.g., T. Kottos and H. Schanz, Physica E {\bf 9}, 523 (2001)].
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Based on earlier work on regular quantum graphs we show that a large class of scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos and quantum chaotic systems are not usually explicitly analytically solvable.
With Hubbard model, the entanglement scaling behavior in a two-dimensional itinerant system is investigated. It has been found that, on the two sides of the critical point denoting an inherent quantum phase transition (QPT), the entanglement follows different scalings with the size just as an order parameter does. This fact reveals the subtle role played by the entanglement in QPT as a fungible physical resource.
Fast-forward scaling theory for quantum dynamics on curved space-time
本文提出弯曲时空量子动力学的快进标度理论，推导出实现速度受控和空间标度动力学的系统参数，揭示了引力作用下的标度性质。
We show that a scaling law exists for the near resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasi-classical phase-space representation of the quantum system with noise allows a new scaling law to be deduced. The scaling law and associated stability are confirmed by comparison with quantum simulations and experimental data.
We report on a time scaling technique to enhance the performances of quantum protocols in non-Hermitian systems. The considered time scaling involves no extra-couplings and yields a significant enhancement of the quantum fidelity for a comparable amount of resources. We discuss the application of this technique to quantum state transfers in 2 and 3-level open quantum systems. We derive the quantum speed limit in a system governed by a non-Hermitian Hamiltonian. Interestingly, we show that, with an appropriate driving, the time-scaling technique preserves the optimality of the quantum speed wit…
We present an exact analytical solution of the spectral problem of quasi one-dimensional scaling quantum graphs. Strongly stochastic in the classical limit, these systems are frequently employed as models of quantum chaos. We show that despite their classical stochasticity all scaling quantum graphs are explicitly solvable in the form $E_n=f(n)$, where $n$ is the sequence number of the energy level of the quantum graph and $f$ is a known function, which depends only on the physical and geometrical properties of the quantum graph. Our method of solution motivates a new classification scheme for…
The quantum repeater protocol is a promising approach to implement long-distance quantum communication and large-scale quantum networks. A key idea of the quantum repeater protocol is to use long-lived quantum memories to achieve efficient entanglement connection between different repeater segments with a polynomial scaling. Here we report an experiment which realizes efficient connection of two quantum repeater segments via on-demand entanglement swapping by the use of two atomic quantum memories with storage time of tens of milliseconds. With the memory enhancement, scaling-changing accelera…
Scaling Laws for Hybrid Quantum Neural Networks: Depth, Width, and Quantum-Centric Diagnostics
研究混合量子-经典分类器在深度和量子比特数量变化下的性能与量子行为扩展规律，通过多个数据集评估预测性能及量子特性，揭示扩展趋势、饱和区域及数据集依赖性。
A simple quantum simulation algorithm with near-optimal precision scaling
本文提出了一种简单且具有近最优精度缩放的量子模拟算法，适用于早期容错量子硬件。
In many-body quantum systems, the quantum Fisher information an observer can obtain is susceptible to decoherence. Consequently, quantum enhanced metrology, such as Heisenberg scaling, cannot usually be achieved. We show, via two distinct methods, that by applying periodic quantum error corrections, we can achieve the Heisenberg scaling for an extended period of time on a three-qubit Tavis-Cumming Model, where three two-level atoms interact with a single cavity mode, under certain approximations. The generalization to arbitrary number of atoms case is also discussed.
We present a finite-size scaling analysis of the entanglement in a two-dimensional arrays of quantum dots modeled by the Hubbard Hamiltonian on a triangular lattice. Using multistage block renormalization group approach, we have found that there is an abrupt jump of the entanglement when a first-order quantum phase transition occurs. At the critical point, the entanglement is constant, independent of the block size.
Whether noisy quantum devices without error correction can provide quantum advantage over classical computers is a critical issue of current quantum computation. In this work, the random quantum circuits, which are used as the paradigm model to demonstrate quantum advantage, are simulated with depolarizing noise on experiment relevant two-dimensional architecture. With comprehensive numerical simulation and theoretical analysis, we find that the maximum achievable operator entanglement entropy, which indicates maximal simulation cost, has area law scaling with the system size for constant nois…
The explicit solution to the spectral problem of quantum graphs is used to obtain the exact distributions of several spectral statistics, such as the oscillations of the quantum momentum eigenvalues around the average, $δk_{n}=k_{n}-\bar k_{n}$, and the nearest neighbor separations, $s_{n}=k_{n}-k_{n-1}$.
Fundamental Scaling Limit in Critical Quantum Metrology
本研究建立了临界量子计量中量子Fisher信息随总演化时间的基本标度极限，发现卷绕数决定标度界限，并通过时间相关控制实现指数标度，且该标度在未达临界点及热耗散下仍成立。
Observable Scaling Hierarchies in Multiphoton Dissipative Quantum Sensing
该研究探究压缩驱动场的量子关联对耗散多光子量子传感标度定律的影响，发现独立与联合压缩场对应不同标度，正规序可观测量的有效非线性阶次会减少1，为基于结构化压缩光的量子传感协议提供设计原则。
We propose a method to achieve scalable quantum computation based on fast quantum gates on an array of trapped ions, without the requirement of ion shuttling. Conditional quantum gates are obtained for any neighboring ions through spin-dependent acceleration of the ions from periodic photon kicks. The gates are shown to be robust to influence of all the other ions in the array and insensitive to the ions' temperature.
Using the concept of spectral engineering we explore the possibilities of building potentials with prescribed spectra offered by a modified intertwining technique involving operators which are the product of a standard first-order intertwiner and a unitary scaling. In the same context we study the iterations of such transformations finding that the scaling intertwining provides a different and richer mechanism in designing quantum spectra with respect to that given by the standard intertwining
We numerically investigated the quantum-classical transition in rf-SQUID systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent $λ_{m}$, exhibits non-monotonic behavior as a function of the coupling strength $D$. By measuring the proximity of quantum and classical evolution with the uncertainty of dynamics, we show that the uncertainty is a monotonic function of $λ_{m}/D$. In addition, the scaling holds in SQUID systems to a relatively smaller $\hbar_{eff}$, suggesting the universality for this scaling.
We numerically study quantum adiabatic algorithm for the propositional satisfiability. A new class of previously unknown hard instances is identified among random problems. We numerically find that the running time for such instances grows exponentially with their size. Worst case complexity of quantum adiabatic algorithm therefore seems to be exponential.
Quantum Fisher information (QFI) of the reduced two-atom state is employed to capture the quantum criticality of the superradiant phase transition in the Dicke model in the infinite size and finite-$N$ systems respectively. The analytical expression of the QFI of its ground state is evaluated explicitly. And finite-size scaling analysis is performed with the large accessible system size due to the effective bosonic coherent-state technique. We also investigate the large-size scaling behavior of the scaled QFI of the reduced $N$-atom state and show the accurate exponent.
It is well known that in a quantum phase transition (QPT), entanglement remains short ranged [Osterloh et al., Nature 416 608-610 (2005)]. We ask if there is a quantum property entailing the whole system which diverges near this point. Using the recently proposed measures of quantum macroscopisity, we show that near a quantum critical point, it is the effective size of macroscopic superposition between the two symmetry breaking states which grows to the scale of system size and its derivative with respect to the coupling shows both singular behavior and scaling properties.
This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, i. e. unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic scaling exponent of the second moment of the walk i. e. of the mean squared distance covered by a walk. As the quantum stochastic walk model encompasses both classical random walks and quantum walks, we are interested how the continuous change from one regime to the other influences the asymptotic scaling exponent. Moreover this model allows for behavior which is …
We consider the usage of dynamical decoupling in quantum metrology, where the joint evolution of system plus environment is described by a Hamiltonian. We demonstrate that by ultra-fast unitary control operations acting locally only on system qubits, essentially all kinds of noise can be eliminated. This is done in such a way that the desired evolution is reduced by at most a constant factor, leading to Heisenberg scaling. The only exception is noise that is generated by the Hamiltonian to be estimated itself. However, even for such parallel noise, one can achieve an improved scaling as compar…
Performance and scaling analysis of variational quantum simulation
本文通过比较变分量子模拟与非变分方法，分析了量子电路深度随系统规模和模拟时间的扩展特性，并讨论了相应的经典复杂性。
Critical Scaling of the Quantum Wasserstein Distance
研究量子临界系统基态间量子瓦瑟斯坦距离的临界标度特性，通过转子场异斯模型验证临界指数。
This manuscript, presented to receive habilitated doctor degree, contains an overview of my recent works in developing complex scaling method and its applications in the few-body physics.
We study the driven critical dynamics with an equilibrium initial state near a quantum critical point. In contrast to the original Kibble-Zurek mechanism, which describes the driven dynamics starting from an adiabatic stage that is far from the critical point, the initial adiabacity is broken in this scenario. As a result, the scaling behavior cannot be described by the original Kibble-Zurek scaling. In this work we propose a scaling theory, which includes the initial parameters as additional scaling variables, to characterize the scaling behavior. In particular, this scaling theory can be use…
We study the scaling of quantum discord (a measure of quantum correlation beyond entanglement) in spin models analytically and systematically. We find that at finite temperature the block scaling of quantum discord satisfies an area law for any two-local Hamiltonian. We show that generically and heuristically the two-site scaling of quantum discord is similar to that of correlation functions. In particular, at zero temperature it decays exponentially and polynomially in gapped and gapless (critical) systems, respectively; at finite temperature it decays exponentially in both gapped and gapless…
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than non-critical states. Standard algorithms for one-dimensional many-particle systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality: the scaling theory of finite entanglement is only superficially similar to finite-size scaling, and has a different physical o…
We investigate the scaling and spatial distribution of genuine multiparticle entanglement in three- and four-spin reduced states of the one-dimensional XY-model at the quantum phase transition. We observe a logarithmic divergence and show that genuine three- and four-particle entanglement obeys finite-size scaling.
In this paper, we consider Szegedy's walk, a type of discrete time quantum walk, and corresponding continuous time quantum walk related to the birth and death chain. We show that the scaling limit of time averaged distribution for the continuous time quantum walk induces that of Szegedy's walk if there exists the spectral gap on so-called the corresponding Jacobi matrix .
We predict that exploiting spin-orbit coupling in a harmonically trapped spinor quantum gas can lead to scaling of the optimal measurement precision beyond the Heisenberg scaling. We show that quadratic scaling with the number of atoms can be facilitated via squeezed center-of-mass excitations of the atomic motion using a 1D spin-orbit coupled fermions or strongly interacting bosons (Tonks-Girardeau gas). Based on predictions derived from analytic calculations of the corresponding quantum Fisher information, we then introduce a protocol which overcomes the Heisenberg scaling (and limit) with h…
Dynamical quantum phase transitions (DQPTs) at critical times appear as non-analyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPT…
We investigate the emergence of universal dynamical scaling in quantum critical spin systems adiabatically driven out of equilibrium, with emphasis on quench dynamics which involves non-isolated critical points (i.e., critical regions) and cannot be a priori described through standard scaling arguments nor time-dependent perturbative approaches. Comparing to the case of an isolated quantum critical point, we find that non-equilibrium scaling behavior of a large class of physical observables may still be explained in terms of equilibrium critical exponents. However, the latter are in general no…
We investigate non-equilibrium dynamical scaling in adiabatic quench processes across quantum multicritical points. Our analysis shows that the resulting power-law scaling depends sensitively on the control path, and that anomalous critical exponents may emerge depending on the universality class. We argue that the observed anomalous behavior originates in the fact that the dynamical excitation process takes place asymmetrically with respect to the static multicritical point, and that non-critical energy modes may play a dominant role. As a consequence, dynamical scaling requires introducing n…
The Faddeev two body bound state model is discussed as an example of a QCD inspired model thought by some to exhibit dimensional transmutation. This simple model is solved exactly and the growth of a specified dimensional energy scale is shown to be an illusion.
In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework of scaling theory. Further, we reveal a profound difference between classical correlations and the non-local quantum correlation, entanglement: the correlation length diverges at the phase transition, whereas entanglement in general remains short ranged.
Artificial magnetic molecules can contribute to progressing towards large scale quantum computation by: a) integrating multiple quantum resources and b) reducing the computational costs of some applications. Chemical design, guided by theoretical proposals, allows embedding nontrivial quantum functionalities in each molecular unit, which then acts as a microscopic quantum processor able to encode error protected logical qubits or to implement quantum simulations. Scaling up even further requires 'wiring-up' multiple molecules. We discuss how to achieve this goal by the coupling to on-chip supe…
Quantum fluctuations of a certain class of bulk operators defined in spatial sub-volumes of Minkowski space-time, have an unexpected area scaling property. We wish to present evidence that such area scaling may be ascribed to a boundary theory. We first highlight the implications of area scaling with two examples in which the boundary area of the spatial regions is not monotonous with their volume. Next, we prove that the covariance of two operators that are restricted to two different regions in Minkowski space scales linearly with their mutual boundary area. Finally, we present an example wh…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems with time-independent Hamiltonians. The mapping of dynamics can be performed in any dimension, for an arbitrary number of interacting particles and for any type of the scaling interaction potential. The exact solvability of a "dual" time-independent Hamiltonian automatically means the exact solvability of the original problem with model time-dependence.
We present a general method, based on a multiple-scale approach, for deriving the perturbative solutions of the scaling equations governing the expansion of superfluid ultracold quantum gases released from elongated harmonic traps. We discuss how to treat the secular terms appearing in the usual naive expansion in the trap asymmetry parameter epsilon, and calculate the next-to-leading correction for the asymptotic aspect ratio, with significant improvement over the previous proposals.
Unique and Universal scaling in dynamical quantum phase transitions
本文揭示了缓慢驱动的动力学量子相变中临界时间与淬火速率呈幂律标度关系，其指数由普适类决定，并基于 Kibble-Zurek 机制验证了该标度在单粒子、多体及厄米与非厄米系统中的普适性。
In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum co…
Universal Family-Vicsek scaling in quantum gases far from equilibrium
研究发现量子多体系统中存在经典表面生长的通用缩放行为，通过观测一维玻色气体的粒子数涨落，验证了FV缩放的普遍性。
The entanglement spectrum describing quantum correlations in many-body systems has been recently recognized as a key tool to characterize different quantum phases, including topological ones. Here we derive its analytically scaling properties in the vicinity of some integrable quantum phase transitions and extend our studies also to non integrable quantum phase transitions in one dimensional spin models numerically. Our analysis shows that, in all studied cases, the scaling of the difference between the two largest non degenerate Schmidt eigenvalues yields with good accuracy critical points an…
The thermodynamic properties of ideal quantum gases are derived solely from dimensional arguments, the Pauli principle and thermodynamic relations, without resorting to statistical mechanics.
The scaling of the entanglement entropy at a quantum critical point allows us to extract universal properties of the state, e.g., the central charge of a conformal field theory. With the rapid improvement of noisy intermediate-scale quantum (NISQ) devices, these quantum computers present themselves as a powerful tool to study critical many-body systems. We use finite-depth quantum circuits suitable for NISQ devices as a variational ansatz to represent ground states of critical, infinite systems. We find universal finite-depth scaling relations for these circuits and verify them numerically at …
Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge $Q$ and scaling dimension $Δ$. For the simplest states (such as the Laughlin series) the scaling dimension determines the quasiparticle's anyonic statistics (the statistical phase $θ=2πΔ$). For more complicated states (featuring counterpropagating modes or non-Abelian statistics) knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases knowing the scaling dimension facilitates distinguishing different candidate theories for des…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on long-range quantum spin models that illustrate this scaling behaviour, and provide indications for its common occurrence by making use of Lieb-Robinson bounds. I argue that these findings may help in understanding the extraordinarily short equilibration timescales predicted by typicality techniques.
A summary of number structure scaling is followed by a description of the effects of number scaling in nonrelativistic quantum mechanics. The description extends earlier work to include the effects on the states of two or more interacting particles. Emphasis is placed on the effects on entangled states. The resulting scaling field is generalized to describe the effects on these states. It is also seen that one can use fiber bundles with fibers associated with single locations of the underlying space to describe the effects of scaling on arbitrary numbers of particles.
Global quantum quench with a finite quench rate which crosses critical points is known to lead to universal scaling of correlation functions as functions of the quench rate. In this work, we explore scaling properties of the entanglement entropy of a subsystem in a harmonic chain during a mass quench which asymptotes to finite constant values at early and late times and for which the dynamics is exactly solvable. When the initial state is the ground state, we find that for large enough subsystem sizes the entanglement entropy becomes independent of size. This is consistent with Kibble-Zurek sc…
Anomalous Dynamical Scaling at Topological Quantum Criticality
研究拓扑非平凡量子临界点的非平衡驱动动力学，发现临界拓扑边缘模式导致异常动力学标度行为，通过分析量子自旋链中不同拓扑QCP的bulk和边界序参量驱动动力学，证明bulk动力学遵循传统KZ标度，而拓扑临界点的边界动力学具有独特修改标度关系。
The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work…
Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical point (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J$-$Q_3$ model. In this work, we study the nonequilibrium imaginary-time relaxation dynamics in the $J$-$Q_2$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point, but also investigate the breakdown and the vestige o…
We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies' wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. In particular, lattice fields are identified with the continuum field smeared with Daubechies'…
We study the destruction of dynamical localization, experimentally observed in an atomic realization of the kicked rotor, by a deterministic Hamiltonian perturbation, with a temporal periodicity incommensurate with the principal driving. We show that the destruction is gradual, with well defined scaling laws for the various classical and quantum parameters, in sharp contrast with predictions based on the analogy with Anderson localization.
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