Quantum simulation of operator spreading in the chaotic Ising model

TL;DR

This paper demonstrates the use of IBM quantum computers to simulate operator spreading in a 4-spin Ising model, revealing ballistic spreading in chaos and localization in integrability, advancing quantum simulation techniques.

Contribution

It introduces a physically motivated fixed-node OTOC method enabling high-fidelity simulation of operator spreading on cloud quantum hardware.

Findings

Ballistic operator spreading observed in chaotic regime

Operator localization detected in integrable regime

Effective use of error mitigation and Trotterization techniques

Abstract

There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a 4-spin Ising model as a function of space, time, and integrability. Reaching 4 spins while retaining high circuit fidelity is made possible by the use of a physically motivated fixed-node variant of the OTOC, allowing scrambling to be estimated without overhead. We find clear signatures of ballistic operator spreading in a chaotic regime, as well as operator localization in an integrable regime. The techniques developed and demonstrated here open up the possibility of using cloud-based quantum computers to study and visualize scrambling phenomena, as well as quantum information dynamics more generally.