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arXiv:2410.10794 · Physical Review Research

Robustness of near-thermal dynamics on digital quantum computers

Eli Chertkov, Yi‐Hsiang Chen, Michael Lubasch, David Hayes, Michael Foss‐Feig

Published Jan 21, 2026• 1 citation
arXivHTMLPDF

Abstract

Understanding the impact of gate errors on quantum circuits is crucial to determining the potential applications of quantum computers, especially in the absence of large-scale error-corrected hardware. We put forward analytical arguments, corroborated by extensive numerical and experimental evidence, that Trotterized quantum circuits simulating the time evolution of systems near thermal equilibrium are substantially more robust to both quantum gate errors and Trotter (discretization) errors than is widely assumed. In Quantinuum’s trapped-ion computers, the weakly entangling gates that appear in Trotterized circuits can be implemented natively, and their error rate is smaller when they generate less entanglement; from benchmarking, we know that the error for a gate exp [ − i ( Z ⊗ Z ) τ ] decreases roughly linearly with τ , up to a small offset at τ = 0 . We provide extensive evidence that this scaling, together with the robustness of near-thermal dynamics to both gate and discretization errors, facilitates substantial improvements in the achievable accuracy of Trotterized dynamics on near-term quantum computers. We make heavy use of a theoretical tool—a statistical ensemble of random product states that approximates a thermal state, which can be efficiently prepared with low noise on quantum computers. We outline how the random product state ensemble can be used to predict, optimize, and design Hamiltonian simulation experiments on near-thermal quantum systems.

DOI
10.1103/nn2w-jxpf

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Understanding the impact of gate errors on quantum circuits is crucial to determining the potential applications of quantum computers, especially in the absence of large-scale error-corrected hardware. We put forward analytical arguments, corroborated by extensive numerical and experimental evidence, that Trotterized quantum circuits simulating the time evolution of systems near thermal equilibrium are substantially more robust to both quantum gate errors and Trotter (discretization) errors than is widely assumed. In Quantinuum’s trapped-ion computers, the weakly entangling gates that appear in Trotterized circuits can be implemented natively, and their error rate is smaller when they generate less entanglement; from benchmarking, we know that the error for a gate exp [ − i ( Z ⊗ Z ) τ ] decreases roughly linearly with τ , up to a small offset at τ = 0 . We provide extensive evidence that this scaling, together with the robustness of near-thermal dynamics to both gate and discretization errors, facilitates substantial improvements in the achievable accuracy of Trotterized dynamics on near-term quantum computers. We make heavy use of a theoretical tool—a statistical ensemble of random product states that approximates a thermal state, which can be efficiently prepared with low noise on quantum computers. We outline how the random product state ensemble can be used to predict, optimize, and design Hamiltonian simulation experiments on near-thermal quantum systems.
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.
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.
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.
Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the randomization of Suzuki-Trotter product formulas have been shown to be a powerful approach to reducing the errors of quantum simulation and lowering the gate count. In this paper, we study the performance of non-unitary simulation channels and consider the error structure of channels constructed from a weighted average of unitary circuits. We show that averaging over just a few simulation circuits can significantly reduce the Trotterization error for both single-step short-time and multi-step long-time simulations. We focus our analysis on two approaches for constructing circuit ensembles for averaging: (i) permuting the order of the terms in the Hamiltonian and (ii) applying a set of global symmetry transformations. We compare our analytical error bounds to empirical performance and show that empirical error reduction surpasses our analytical estimates in most cases. Finally, we test our method on an IonQ trapped-ion quantum computer accessed via the Amazon Braket cloud platform, and benchmark the performance of the averaging approach.
We consider the problem of preparing thermal equilibrium states at finite temperature on quantum computers. Assuming thermalization, we show that states that are locally at thermal equilibrium can be prepared by evolving adiabatically an initial thermal Gibbs state of a simple Hamiltonian with an interpolating time-dependent Hamiltonian, identically to adiabatic ground state preparation. We argue that the entropy density of local density matrices is conserved during the adiabatic evolution in the thermodynamic limit, so that both the entropy and energy of the final state can be computed, and thus the final temperature too. We show that in the presence of hardware noise, the entropy created by the noisy evolution can be precisely benchmarked with mirror circuits. We give numerical evidence that the resulting thermal state preparation protocol is noise-resilient for depolarizing noise, in the sense that the energy-temperature curve measured on a noisy quantum computer is remarkably insensitive to the amplitude of depolarizing noise in the state preparation. We finally propose a protocol to estimate the lack of adiabaticity in a given actual Trotter implementation of the dynamics. We test our protocol on Quantinuum’s H1-1 ion-trap device. We measure that a circuit with 640 two-qubit gates implemented on hardware generates an entropy per site of 0.166 ± 0.0045, giving a benchmark metric for this state preparation. We report the preparation of a thermal state with temperature 2.56 ± 0.26 of the Ising model in size 5 × 4.
The simulation of adiabatic evolution has deep connections with adiabatic quantum computation, the quantum approximate optimization algorithm, and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. We show that with additional conditions, the circuit depth can be linear in simulation time TTT. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: (1) The fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. (2) Because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. (3) As the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.