Benchmarking quantum chaos from geometric complexity

TL;DR

This paper explores how geometric complexity can serve as an indicator of quantum chaos by analyzing the circuit complexity of a non-Gaussian bosonic system's time-evolution operator.

Contribution

It introduces a new method to study geometric complexity in non-Gaussian quantum systems for benchmarking quantum chaos.

Findings

Geometric complexity correlates with quantum chaos indicators.

Complexity can serve as a diagnostic tool for quantum chaos.

Results support geometric complexity as a useful chaos benchmark.

Abstract

Recent studies have shown that there is a strong interplay between quantum complexity and quantum chaos. In this work, we consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems to benchmark the quantum chaos in a well-known oscillator model. In particular, we study the circuit complexity for the unitary time-evolution operator of a non-Gaussian bosonic quantum mechanical system. Our results indicate that, within some limitations, geometric complexity can indeed be a good indicator of quantum chaos.