Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits

TL;DR

This paper introduces a method using random circuits on NISQ devices to simulate quantum hydrodynamics, demonstrating robustness to errors and potential for practical transport coefficient extraction in near-term quantum hardware.

Contribution

It proposes a novel algorithm combining random circuits with Trotterized evolution for hydrodynamics simulation on noisy quantum devices, showing robustness to errors and scalability.

Findings

Hydrodynamic correlations are robust against Trotter step size.

Meaningful results are achievable with realistic error rates on NISQ hardware.

Random circuits are effective for simulating quantum many-body dynamics.

Abstract

In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.