Simulating quantum chaos on a quantum computer

TL;DR

This paper demonstrates how NISQ quantum computers can simulate chaotic quantum systems like the quantum kicked top, revealing chaos signatures and entanglement dynamics without increasing gate complexity.

Contribution

Introduces a hybrid classical-quantum approach for simulating quantum chaos on NISQ devices, enabling exploration of all chaotic regimes and arbitrary evolution lengths.

Findings

Observed periodicities in 2-qubit QKT evolution.

Detected signatures of chaos in entanglement dynamics.

Confirmed link between entanglement and delocalization.

Abstract

We show that currently available noisy intermediate-scale quantum (NISQ) computers can be used for versatile quantum simulations of chaotic systems. We introduce a novel classical-quantum hybrid approachfor exploring the dynamics of the chaotic quantum kicked top (QKT) on a universal quantum computer. The programmability of this approach allows us to experimentally explore the complete range of QKT chaoticity parameter regimes inaccessible to previous studies. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer (IBMQ), we observe periodicities in the evolution of the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit entanglement. We also demonstrate a connection between entanglement and delocalization in the 2-qubit QKT, confirming theoretical predictions.