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arXiv:2303.08461 · PRX Quantum

Simulating Prethermalization Using Near-Term Quantum Computers

Yilun Yang, Arthur Christianen, Sandra Coll-Vinent, Vadim Smelyanskiy, Mari Carmen Bañuls, Thomas E. O’Brien, Dominik S. Wild, J. I. Cirac

Published Aug 11, 2023• 19 citations
arXivHTMLPDF

Abstract

Quantum simulation is one of the most promising scientific applications of quantum computers.Due to decoherence and noise in current devices, it is however challenging to perform digital quantum simulation in a regime that is intractable with classical computers.In this work, we propose an experimental protocol for probing dynamics and equilibrium properties on near-term digital quantum computers.As a key ingredient of our work, we show that it is possible to study thermalization even with a relatively coarse Trotter decomposition of the Hamiltonian evolution of interest.Even though the step size is too large to permit a rigorous bound on the Trotter error, we observe that the system prethermalizes in accordance with previous results for Floquet systems.The dynamics closely resemble the thermalization of the model underlying the Trotterization up to long times.We make our approach resilient to noise by developing an error mitigation scheme based on measurement and rescaling of survival probabilities, which is applicable to time-evolution problems in general.We demonstrate the effectiveness of the entire protocol by applying it to the two-dimensional XY model and we numerically verify its performance with realistic noise parameters for superconducting quantum devices.Our proposal thus provides a route to achieving quantum advantage for relevant problems in condensed-matter physics.

DOI
10.1103/prxquantum.4.030320

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Quantum simulation is one of the most promising scientific applications of quantum computers.Due to decoherence and noise in current devices, it is however challenging to perform digital quantum simulation in a regime that is intractable with classical computers.In this work, we propose an experimental protocol for probing dynamics and equilibrium properties on near-term digital quantum computers.As a key ingredient of our work, we show that it is possible to study thermalization even with a relatively coarse Trotter decomposition of the Hamiltonian evolution of interest.Even though the step size is too large to permit a rigorous bound on the Trotter error, we observe that the system prethermalizes in accordance with previous results for Floquet systems.The dynamics closely resemble the thermalization of the model underlying the Trotterization up to long times.We make our approach resilient to noise by developing an error mitigation scheme based on measurement and rescaling of survival probabilities, which is applicable to time-evolution problems in general.We demonstrate the effectiveness of the entire protocol by applying it to the two-dimensional XY model and we numerically verify its performance with realistic noise parameters for superconducting quantum devices.Our proposal thus provides a route to achieving quantum advantage for relevant problems in condensed-matter physics.
The simulation of non-equilibrium quantum many-body systems on noisy intermediate-scale quantum (NISQ) processors represents a central challenge and opportunity in modern condensed matter physics. Periodically driven (Floquet) systems can host exotic phases of matter with no equilibrium counterpart, most notably discrete time crystals (DTCs) characterized by spontaneous breaking of discrete time-translation symmetry and robust subharmonic responses. However, the realization of DTCs faces fundamental obstacles: driven many-body systems generically absorb energy and thermalize to an infinite-temperature state, destroying time-crystalline order. Two primary mechanisms have been identified to stabilize DTCs—many-body localization (MBL) through strong disorder, and Floquet prethermalization wherein high-frequency driving suppresses heating over exponentially long timescales. This work investigates the digital quantum simulation of prethermal DTCs on current superconducting quantum processors, with a focus on understanding and mitigating the impact of hardware noise. Recent experiments on 133-qubit heavy-hexagonal devices have demonstrated the realization of clean two-dimensional DTCs and incommensurately modulated DTCs (IM-DTCs) using kicked Ising models, observing period-doubling oscillations persisting for up to 100 Floquet cycles . Crucially, these simulations reveal that quantum noise, often perceived as detrimental, can in certain regimes stabilize novel prethermal DTC phases—a phenomenon identified as noise-induced DTCs supported by symmetry charge pumping or random gate fluctuations . The heavy-hexagonal lattice geometry, compared to square lattices, exhibits significantly slower quantum scrambling, thereby extending the prethermal plateau and enhancing DTC stability. We address two key challenges limiting the scalability of DTC simulations: limited qubit connectivity and environmental noise. By leveraging the universality of native gate sets, we demonstrate how to implement effective couplings among physically disconnected qubits at the cost of increased circuit depth, enabling the study of interaction-range effects on DTC stabilization—a phenomenon previously unobserved experimentally . Furthermore, we benchmark the performance of error mitigation protocols based on depolarising noise models, achieving excellent agreement between error-mitigated hardware data and tensor-network simulations in regimes where classical computations remain tractable . Our results highlight the complementary roles of quantum hardware and classical simulation: quantum processors provide access to regimes where entanglement growth outpaces tensor-network methods, while careful validation against classical benchmarks ensures the reliability of quantum outcomes. This study establishes a concrete pathway for using NISQ devices as experimental platforms for synthesizing and probing novel non-equilibrium quantum phases, advancing both our fundamental understanding of Floquet many-body dynamics and the practical capabilities of quantum simulation. The identification of noise as an active ingredient in phase stabilization suggests new directions for quantum engineering of spatiotemporal orders on near-term hardware.
Simulating nonequilibirum dynamics of a quantum many-body system is one of the promising applications of quantum computing. We simulate the time evolution of one-dimensional Z 2 lattice gauge theory on IBM’s superconducting 156-qubit device, ibm_fez. We consider the Floquet circuit made of the Trotter decomposition of Hamiltonian evolution and focus on its dynamics toward thermalization. Quantum simulation with the help of error mitigation is successful in running the Floquet circuit made of 38 and 116 qubits up to 10 Trotter steps in the best case. This is enough to reach the early stage of prethermalization. Our work would be a benchmark for the potential power of quantum computing for high-energy physics problems. Published by the American Physical Society 2024
Abstract Emulating thermal observables on a digital quantum computer is essential for quantum simulation of many-body physics. However, thermalization typically requires a large system size due to incorporating a thermal bath, whilst limited resources of near-term digital quantum processors allow for simulating relatively small systems. We show that thermal observables and fluctuations may be obtained for a small closed system without a thermal bath. Thermal observables occur upon classically averaging quantum mechanical observables over randomized variants of their time evolution that run independently on a digital quantum processor. Using an IBM quantum computer, we experimentally find thermal occupation probabilities with finite positive and negative temperatures defined by the initial state’s energy. Averaging over random evolutions facilitates error mitigation, with the noise contributing to the temperature in the simulated observables. This result fosters probing the dynamical emergence of equilibrium properties of matter at finite temperatures on noisy intermediate-scale quantum hardware.
The Suzuki-Trotter decomposition, which digitalizes quantum time evolution, provides a promising framework for simulating quantum dynamics on quantum hardware and exploring quantum advantage over classical computation. However, conventional Trotter circuits require a large number of non-local gates, lowering their faithfulness to the ideal dynamics when implemented on current noisy quantum hardware. While most previous studies have focused on circuit optimization, we instead propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices. Our method substantially reduces both the residual error by Trotter decomposition and the number of CNOT operations compared to conventional Trotter decompositions by exploiting the symmetry of the target model to construct an effective Hamiltonian with fewer two-qubit gates. We demonstrate the noise robustness of the proposed approach through numerical simulations of a nine-site Heisenberg model under realistic noise, and further validate its experimental practicality on the IBM superconducting device, achieving a state fidelity exceeding 0.980.980.98 when combined with quantum error mitigation in the three-site case. The proposed circuit design is also compatible with existing circuit optimization techniques. Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.
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.
The Suzuki–Trotter decomposition, which digitalizes quantum time evolution, provides a promising framework for simulating quantum dynamics on quantum hardware and exploring quantum advantage over classical computation. However, conventional Trotter circuits require a large number of non-local gates, lowering their faithfulness to the ideal dynamics when implemented on current noisy quantum hardware. While most previous studies have focused on circuit optimization, we instead propose a new Trotter decomposition that is intrinsically circuit-efficient for simulating quantum dynamics on near-term devices. Our method substantially reduces both the residual error by Trotter decomposition and the number of CNOT operations compared to conventional Trotter decompositions by exploiting the symmetry of the target model to construct an effective Hamiltonian with fewer two-qubit gates. We demonstrate the noise robustness of the proposed approach through numerical simulations of a nine-site Heisenberg model under realistic noise and further validate its experimental practicality on the IBM superconducting device, achieving a state fidelity exceeding 0.98 when combined with quantum error mitigation in the three-site case. The proposed circuit design is also compatible with existing circuit optimization techniques. Our results establish a practical route toward noise-resilient quantum simulation in many-body dynamics.