Dynamical simulations of many-body quantum chaos on a quantum computer

Abstract

Quantum circuits with local unitaries have emerged as a rich playground for the exploration of many-body quantum dynamics of discrete-time systems. While the intrinsic locality makes them particularly suited to run on current quantum processors, the task of verification at non-trivial scales is complicated for non-integrable systems. Here, we study a special class of maximally chaotic circuits known as dual unitary circuits -- exhibiting unitarity in both space and time -- that are known to have exact analytical solutions for certain correlation functions. With advances in noise learning and the implementation of novel error mitigation methods, we show that a superconducting quantum processor with 91 qubits is able to accurately simulate these correlators. We then probe dynamics beyond exact verification, by perturbing the circuits away from the dual unitary point, and compare our results to classical approximations with tensor networks. These results cement error-mitigated digital quantum simulation on pre-fault-tolerant quantum processors as a trustworthy platform for the exploration and discovery of novel emergent quantum many-body phases.