In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.
We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. In the limit when fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure and we study the quantum computer core (central band) with the highest density of states. Above a critical inter-qubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of eigenstates in an isolated quantum computer. The onset of chaos results in the interactio…
Local Thermalization of SU(2) Lattice Gauge Fields on Quantum Computers
National Taiwan University（国立台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；University of Washington（华盛顿大学）；Duke University（杜克大学）；Universität Regensburg（雷根斯堡大学）
We show that certain coherences, termed as heat-exchange coherences, which contribute to the thermalization process of a quantum probe in a repeated interactions scheme, can modify the spectral response of the probe system. We suggest to use the power spectrum as a way to experimentally assess the apparent temperature of non-thermal atomic clusters carrying such coherences and also prove that it is useful to measure the corresponding thermalization time of the probe, assuming some information is provided on the nature of the bath. We explore this idea in two examples in which the probe is assu…
The investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and …
Weakly interacting quantum fluids allow for a natural kinetic theory description which takes into account the fermionic or bosonic nature of the interacting particles. In the simplest cases, one arrives at the Boltzmann-Nordheim equations for the reduced density matrix of the fluid. We discuss here two related topics: the kinetic theory of the fermionic Hubbard model, in which conservation of total spin results in an additional Vlasov type term in the Boltzmann equation, and the relation between kinetic theory and thermalization.
We study the time evolution of occupation numbers for interacting Fermi-particles in the situation when exact compound states are "chaotic". This situation is generic for highly excited many-particles states in heavy nuclei, complex atoms, quantum dots, spin systems and quantum computer models. Numerical data show perfect agreement with a simple theory for the onset of thermalization in close systems of interacting particles.
We present a quantum algorithm to prepare the thermal Gibbs state of interacting quantum systems. This algorithm sets a universal upper bound D^alpha on the thermalization time of a quantum system, where D is the system's Hilbert space dimension and alpha < 1/2 is proportional to the Helmholtz free energy density of the system. We also derive an algorithm to evaluate the partition function of a quantum system in a time proportional to the system's thermalization time and inversely proportional to the targeted accuracy squared.
Isolated quantum many-body systems with integrable dynamics generically do not thermalize when taken far from equilibrium. As one perturbs such systems away from the integrable point, thermalization sets in, but the nature of the crossover from integrable to thermalizing behavior is an unresolved and actively discussed question. We explore this question by studying the dynamics of the momentum distribution function in a dipolar quantum Newton's cradle consisting of highly magnetic dysprosium atoms. This is accomplished by creating the first one-dimensional Bose gas with strong magnetic dipole-…
The last decade has witnessed the remarkable progress in our understanding of thermalization in isolated quantum systems. Combining the eigenstate thermalization hypothesis with quantum measurement theory, we extend the framework of quantum thermalization to open many-body systems. A generic many-body system subject to continuous observation is shown to thermalize at a single trajectory level. We show that the nonunitary nature of quantum measurement causes several unique thermalization mechanisms that are unseen in isolated systems. We present numerical evidence for our findings by applying o…
Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly-interacting quantum systems. Recent matrix product operator methods have made simulations of quantum hydrodynamics in 1+1d tractable, but they do not naturally generalize to 2+1d or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the…
We present quantitative predictions for quantum simulator experiments on Ising models from trapped ions to Rydberg chains and show how the thermalization, and thus decoherence times, can be controlled by considering common, independent, and end-cap couplings to the bath. We find (i) independent baths enable more rapid thermalization in comparison to a common one; (ii) the thermalization timescale depends strongly on the position in the Ising phase diagram; (iii) for a common bath larger system sizes show a significant slow down in the thermalization process; and (iv) finite-size scaling indica…
We study the role of the system-bath coupling for the generalized canonical thermalization [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein et al., Phys. Rev. Lett. 96, 050403(2006)] that reduces almost all the pure states of the "universe" [formed by a system S plus its surrounding heat bath $B$] to a canonical equilibrium state of S. We present an exactly solvable, but universal model for this kinematic thermalization with an explicit consideration about the energy shell deformation due to the interaction between S and B. By calculating the state numbers of the "universe" and…
Algorithmic Cooling is a method that uses novel data compression techniques and simplecquantum computing devices to improve NMR spectroscopy, and to offer scalable NMR quantum computers. The algorithm recursively employs two steps. A reversible entropy compression of the computation quantum-bits (qubits) of the system and an irreversible heat transfer from the system to the environment through a set of reset qubits that reach thermal relaxation rapidly. Is it possible to experimentally demonstrate algorithmic cooling using existing technology? To allow experimental algorithmic cooling, the the…
Preparing thermal states on a quantum computer can have a variety of applications, from simulating many-body quantum systems to training machine learning models. Variational circuits have been proposed for this task on near-term quantum computers, but several challenges remain, such as finding a scalable cost-function, avoiding the need of purification, and mitigating noise effects. We propose a new algorithm for thermal state preparation that tackles those three challenges by exploiting the noise of quantum circuits. We consider a variational architecture containing a depolarizing channel aft…
We consider the problem of time optimal control of a continuous bosonic quantum system subject to the action of a Markovian dissipation. In particular, we consider the case of a one mode Gaussian quantum system prepared in an arbitrary initial state and which relaxes to the steady state due to the action of the dissipative channel. We assume that the unitary part of the dynamics is represented by Gaussian operations which preserve the Gaussian nature of the quantum state, i.e. arbitrary phase rotations, bounded squeezing and unlimited displacements. In the ideal ansatz of unconstrained quantum…
We study the nonequilibrium dynamics of the quantum Newton's cradle in a one-dimensional (1D) Bose gas in the weakly-interacting quasicondensate regime. This is the opposite regime to the original quantum Newton's cradle experiment of Kinoshita et al. [Nature 440, 900 (2006)], which was realized in the strongly interacting 1D Bose gas. Using finite temperature c-field methods, we calculate the characteristic relaxation rates to the final equilibrium state. Hence, we identify the different dynamical regimes of the system in the parameter space that characterizes the strength of interatomic inte…
Quantum Mpemba-like effect in Unruh thermalization
School of Physics, Xian Jiaotong University（西安交通大学物理学院）；Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong（香港科技大学机械与自动化工程学系）；Department of Physics, Hong Kong University of Science and Technology（香港科技大学物理系）；Hefei National Laboratory（合肥国家实验室）
Recent realization of a kinetically-constrained chain of Rydberg atoms by Bernien et al. [Nature 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work [arXiv:1711.03528] such dynamics was attributed to the existence of "quantum scarred" eigenstates in the many-body spectrum of the experimentally realized model. Here we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs en…
We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperat…
Nature is stingy: Universality of Scrooge ensembles in quantum many-body systems
California Institute of Technology（加州理工学院）；Technology Innovation Institute（技术创新研究所）；National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；AWS Center for Quantum Computing（亚马逊云科技量子计算中心）
Small-world structure of quantum computer hardware
Université Marie et Louis Pasteur（玛丽和路易·巴斯德大学）；CNRS（法国国家科学研究中心）；Institut UTINAM (UMR 6213)（UTINAM研究所）；Univ Toulouse（图卢兹大学）；Laboratoire de Physique Théorique（理论物理实验室）
Set theory reduces all processes to assembly and disassembly. A similar architecture is proposed for nature as quantum computer. It resolves the classical space-time underlying Feynman diagrams into a quantum network of creation and annihilation processes, reducing kinematics to quantum statistics, and regularizing the Lie algebra of the Einstein diffeomorphism group. The usually separate and singular Lie algebras of kinematics, statistics, and conserved currents merge into one regular statistics Lie algebra.
We present simulations of non-equilibrium dynamics of quantum field theories on digital quantum computers. As a representative example, we consider the Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a Yukawa-type interaction to a thermal environment described by a scalar field theory. We use the Hamiltonian formulation of the Schwinger model discretized on a spatial lattice. With the thermal scalar fields traced out, the Schwinger model can be treated as an open quantum system and its real-time dynamics are governed by a Lindblad equation in the Markovian limit. The inte…
Novel dynamical phases that violate ergodicity have been a subject of extensive research in recent years. A periodically driven system is naively expected to lose all memory of its initial state due to thermalization, yet this can be avoided in the presence of many-body localization. A discrete time crystal represents a driven system whose local observables spontaneously break time translation symmetry and retain memory of the initial state indefinitely. Here we report the observation of a discrete time crystal on a chain consisting of 57 superconducting qubits on a state--of--the--art quantum…
In the framework of open quantum systems, we study the internal dynamics of both freely falling and static two-level atoms interacting with quantized conformally coupled massless scalar field in de Sitter spacetime. We find that the atomic transition rates depend on both the nature of de Sitter spacetime and the motion of atoms, interestingly the steady states for both cases are always driven to being purely thermal, regardless of the atomic initial states. This thermalization phenomenon is structurally similar to what happens to an elementary quantum system immersed in a thermal field, and th…
We point out that superconducting quantum computers are prospective for the simulation of the dynamics of spin models far from equilibrium, including nonadiabatic phenomena and quenches. The important advantage of these machines is that they are programmable, so that different spin models can be simulated in the same chip, as well as various initial states can be encoded into it in a controllable way. This opens an opportunity to use superconducting quantum computers in studies of fundamental problems of statistical physics such as the absence or presence of thermalization in the free evolutio…
Do quantum computers already exist in Nature? It is proposed that they do. Photosynthesis is one example in which a 'quantum computer' component may play a role in the 'classical' world of complex biological systems. A 'translation' of the standard metabolic description of the 'front-end' light harvesting complex in photosynthesis into the language of quantum computers is presented. Biological systems represent an untapped resource for thinking about the design and operation of hybrid quantum-classical computers and expanding our current conceptions of what defines a 'quantum computer' in Natu…
My 2018 lecture at the ICA workshop in Singapore dealt with quantum computation as a meeting point of the laws of computation and the laws of quantum mechanics. We described a computational complexity argument against the feasibility of quantum computers: we identified a very low-level complexity class of probability distributions described by noisy intermediate-scale quantum computers, and explained why it would allow neither good-quality quantum error-correction nor a demonstration of "quantum supremacy," namely, the ability of quantum computers to make computations that are impossible or ex…
Construction of virtual quantum states became possible due to the hypothesis on the nature of quantum states quant-ph/0212139. This study considers a stochastic geometrical background (stochastic gravitational background) generating correlation (or, coherency) of various quantum non-interacting objects. In the quantum state virtual model, a simple method of generating of two (or more) dichotomic signals with controlled mutual correlation factor from a single continuous stochastic process is implemented. Basing on the system random number generator of the computer, a model of the stationary ran…
Simulating Thermal Properties of Bose-Hubbard Models on a Quantum Computer
Bocconi University（博科尼大学）；Inria, Télécom Paris – LTCI, Institut Polytechnique de Paris（法国国家信息与自动化研究所，巴黎电信学院-通信与图像处理实验室，巴黎理工学院）；Institute for Quantum Information, RWTH Aachen University（亚琛工业大学量子信息研究所）；Inria, ENS de Lyon, Université Claude Bernard Lyon 1, LIP（法国国家信息与自动化研究所，里昂高等师范学院，克莱伯贝尔·里昂第一大学，计算与图像实验室）
Two models of computer, a quantum and a classical "chemical machine" designed to compute the relevant part of Shor's factoring algorithm are discussed. The comparison shows that the basic quantum features believed to be responsible for the exponential speed-up of quantum computations possess their classical counterparts for the hybrid digital-analog computer. It is argued that the measurement errors which cannot be fully corrected make the computation not efficient for both models.
Physical modeling closes the gap between perception in terms of measurements and abstraction in terms of theoretical models. Physical modeling is a major objective in physics and is generally regarded as a creative process. How good are computers at solving this task? This question is both of philosophical and practical interest because a positive answer would allow an artificial intelligence to understand the physical world. Quantum mechanics is the most fundamental physical theory and there is a deep belief that nature follows the rules of quantum mechanics. Hence, we raise the question whet…
This article focuses on the connection between the possibility of quantum computers, the predictability of complex quantum systems in nature, and the issue of free will.
The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is determined
