Measuring out-of-time-order correlators on a quantum computer based on an irreversibility-susceptibility method

TL;DR

This paper experimentally evaluates out-of-time-ordered correlators (OTOCs) on a quantum computer using three protocols, notably introducing the first implementation of the irreversibility-susceptibility method (ISM) to study quantum chaos.

Contribution

It presents the first experimental demonstration of the ISM for measuring OTOCs on a quantum computer, comparing three protocols and analyzing their effectiveness.

Findings

Validated the ISM as a practical tool for quantum chaos studies

Compared the behaviors of three different OTOC measurement protocols

Provided insights into the advantages and limitations of each method

Abstract

The out-of-time-ordered correlator (OTOC) is a powerful tool for probing quantum information scrambling, a fundamental process by which local information spreads irreversibly throughout a quantum many-body system. Experimentally measuring the OTOC, however, is notoriously challenging due to the need for time-reversed evolution. Here, we present an experimental evaluation of the OTOC on a quantum computer, using three distinct protocols to address this challenge: the rewinding time method (RTM), the weak-measurement method (WMM), and the irreversibility-susceptibility method (ISM). Our experiments investigate the quantum dynamics of an XXZ spin-1/2 chain prepared in a thermal Gibbs state. As a key contribution, we provide the first experimental demonstration of the ISM, using the trapped-ion quantum computer, reimei. We also conduct a detailed comparative analysis of all three methods, revealing method-dependent behaviors in the measured OTOC. This work not only validates these protocols as practical tools for exploring quantum chaos on near-term hardware but also offers crucial insights into their respective advantages and limitations, providing a practical framework for future experimental investigations.