Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analog quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system and further extract multipoint correlations from the output strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of 10 19 and outpacing the most powerful supercomputer in terms of sampling rate by 3 orders of magnitude. The volume law scaling of the Rényi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multipoint correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fail to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of an interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.
Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analog quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system and further extract multipoint correlations from the output strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of 10 19 and outpacing the most powerful supercomputer in terms of sampling rate by 3 orders of magnitude. The volume law scaling of the Rényi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multipoint correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fail to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of an interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.
Abstract A crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can perform a computation task that is classically intractable. A key question is to identify setups that can achieve such goal within current technologies. In this work, we provide formal evidence that sampling bit-strings from a periodic evolution of a unitary drawn from the circular orthogonal ensemble (COE) cannot be efficiently simulated with classical computers. As the statistical properties of COE coincide with a large class of driven analog quantum systems thanks to the Floquet eigenstate thermalization hypothesis, our results indicate the possibility that those driven systems could constitute practical candidates for a sampling quantum advantage. To further support this, we give numerical examples of driven disordered Ising chains and 1D driven Bose–Hubbard model.
Scaling up to a large number of qubits with high-precision control is essential in the demonstrations of quantum computational advantage to exponentially outpace the classical hardware and algorithmic improvements. Here, we develop a two-dimensional programmable superconducting quantum processor, Zuchongzhi, which is composed of 66 functional qubits in a tunable coupling architecture. To characterize the performance of the whole system, we perform random quantum circuits sampling for benchmarking, up to a system size of 56 qubits and 20 cycles. The computational cost of the classical simulation of this task is estimated to be 2-3 orders of magnitude higher than the previous work on 53-qubit Sycamore processor [Nature 574, 505 (2019)NATUAS0028-083610.1038/s41586-019-1666-5. We estimate that the sampling task finished by Zuchongzhi in about 1.2 h will take the most powerful supercomputer at least 8 yr. Our work establishes an unambiguous quantum computational advantage that is infeasible for classical computation in a reasonable amount of time. The high-precision and programmable quantum computing platform opens a new door to explore novel many-body phenomena and implement complex quantum algorithms.
Understanding how isolated quantum many-body systems thermalize remains a central question in modern physics. We study the onset of ergodicity in a two-dimensional disordered Heisenberg Floquet model using digital quantum simulation on IBM's Nighthawk superconducting processor, reaching system sizes of up to 10×10 qubits. We probe ergodicity across different length scales by coarse-graining the system into spatial patches of varying sizes and introducing a measure based on the collision entropy of each patch, enabling a detailed study of when ergodic behavior emerges across scales. The high sampling rate of superconducting quantum processing units, together with an optimal sample estimator, allow us to access patches of sizes up to 3×3. We observe that as the Heisenberg coupling J increases, the noiseless system undergoes a smooth crossover from subergodic to ergodic behavior, with smaller patches approaching their random-matrix-theory values first, thereby revealing a hierarchy across scales. In the region of parameter space where classical tensor-network simulations are reliable, small patches or small values of J, we find excellent agreement with the error-mitigated quantum simulation. Beyond this regime, volume-law entanglement and contraction complexity growth causes the cost of classical methods to rise sharply. Our results open new directions for the use of quantum computers in the study of quantum thermalization.
Current quantum simulation experiments are starting to explore nonequilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and timescales. Therefore, the question emerges as to which observables are best suited to study the dynamics in such quantum many-body systems. Using machine learning techniques, we investigate the dynamics and, in particular, the thermalization behavior of an interacting quantum system that undergoes a nonequilibrium phase transition from an ergodic to a many-body localized phase. We employ supervised and unsupervised training methods to distinguish nonequilibrium from equilibrium data, using the network performance as a probe for the thermalization behavior of the system. We test our methods with experimental snapshots of ultracold atoms taken with a quantum gas microscope. Our results provide a path to analyze highly entangled large-scale quantum states for system sizes where numerical calculations of conventional observables become challenging.
The experimental control and observation of quantum many-body systems has become a reality with the advent of ultracold quantum matter. The high level of isolation of these experiments, together with the development of novel measurement techniques, has revived a fundamental debate concerning the thermal equilibration of isolated quantum systems, commonly named "quantum thermalization". In this thesis we make use of a quantum-gas microscope to explore the thermalizing dynamics of highly isolated systems of ultracold bosonic atoms in optical lattices. The ability to prepare and control quantum systems made up of hundreds of atoms makes it possible to explore regimes that represent a challenge for classical numeric simulations. A major part of this dissertation deals with Bose-Hubbard systems in the presence of quenched disorder. We begin by studying the microscopic properties of its phases near equilibrium, where by tuning the strength of the disorder, observe features consistent with the emergence of a so-called Bose-glass phase. We then continue by preparing states far from equilibrium and exploring their quantum many-body dynamics. In particular, we observe signatures of the phenomenon of "many-body localization", which implies a breakdown of quantum thermalization. In addition, we study whether localized systems can be thermalized via the coupling to a bath of few degrees of freedom, i.e. a quantum bath. We do so by preparing a mixture of two interacting atomic species, where one acts as the bath and the other as the localized system. We do observe delocalizing dynamics for large enough baths, though in regimes of weak coupling localization can survive for extremely long times. The second main topic of this thesis is the thermalization of periodically driven many-body systems, so-called Floquet thermalization. In these systems, the absence of energy conservation eventually brings any initial state into a featureless infinite-temperature one. However, for sufficiently high frequencies this thermalization process can take arbitrarily long times, which can enable the engineering of exotic long-lived prethermal states. We use the high isolation of our system, together with the high sensitivity of quantum-gas microscopy, to measure the heating rates for a range of driving frequencies and interaction regimes. Our results show a dramatic suppression of the heating as the frequency of the drive is increased, which is consistent with theoretical expectations.
Periodically driven interacting quantum many-body systems can exhibit long-lived prethermal dynamics, where local observables retain coherent structure even as entanglement and operator complexity grow. Accessing this regime at the system sizes and times needed to determine physical properties of the prethermal state remains a central challenge: state-of-the-art classical methods become unreliable, while noise in quantum hardware degrades observable expectation values. Here we overcome these limitations for a Floquet Ising magnet realized on a heavy-hex lattice. Using the advanced error mitigation software QESEM on an IBM Heron r3 superconducting quantum processor, we measure magnetization dynamics with percent-level precision and resolve long-lived subharmonic prethermal oscillations in systems of up to 74 qubits. These experiments reach regimes for which leading tensor-network simulations fail to converge, while sparse Pauli-path simulations remain strongly truncation dependent despite extensive computations on advanced GPUs and the Fugaku supercomputer. Leveraging this quantum-accessible regime, we extend finite-size scaling to larger systems and find an unexpectedly slow decrease of the oscillation amplitude with system size, providing strong evidence that this oscillatory response persists in the thermodynamic limit of heavy-hex ladders. A hierarchy of mitigation and validation tests, including unbiased error mitigation, agreement between independent mitigation estimators, noise-model validation on the superconducting hardware, and cross-platform corroboration at selected Floquet cycles on Quantinuum System Model H2 and Quantinuum Helios trapped-ion hardware, supports the reliability of these findings. Our work establishes error-mitigated quantum processors as quantitative scientific instruments for discovering new physics in non-equilibrium quantum matter.