Quantum simulation using Trotterized disorder Hamiltonians in a single-mode optical cavity

TL;DR

This paper introduces a Trotterization-based method to simulate disordered many-body quantum systems with enhanced disorder properties, using a single-mode optical cavity, and analyzes its accuracy and robustness.

Contribution

It presents a novel Trotterization scheme to densify disorder in quantum simulations and proposes a cavity QED implementation of the Sachdev-Ye-Kitaev model.

Findings

Effective model exhibits desired disorder distribution

Trotterization errors are characterized and manageable

Robustness against dissipation is demonstrated

Abstract

All-to-all interacting and disordered many-body systems are notoriously hard to simulate on quantum platforms, as interactions are commonly mediated by auxiliary degrees of freedom that lower the amount of disorder, introducing undesired correlations. In this work, we show how a Trotterization scheme can be effectively utilized to densify the disorder of the model. In particular, we study the statistical properties of the resulting model, as well as Trotterization errors in the simulation that affect the time evolution and dynamical observables. As a concrete example, we propose an implementation via a single-mode cavity QED platform of the complex Sachdev-Ye-Kitaev model. We analyze several features of the effective model, such as the distribution of the effective couplings, the number of interacting sites, state preparation, and the behavior of quantum chaos probes. We conclude this work with a detailed investigation of the robustness of our findings against dissipation, both analytically and numerically.