Exponential speedup in measuring out-of-time-ordered correlators with a single bit of quantum information

TL;DR

This paper introduces a quantum algorithm that significantly accelerates the measurement of out-of-time-ordered correlators, crucial for understanding quantum chaos, by leveraging minimal quantum resources.

Contribution

It presents an efficient quantum algorithm for measuring OTOCs with exponential speed-up, assuming the operator admits an efficient gate decomposition.

Findings

Achieves exponential speed-up over classical methods

Provides a scheme to analyze eigenvalue spectra of OTOCs

Requires only a single qubit of quantum information

Abstract

Out-of-time-ordered correlators (OTOC) are a quantifier of quantum information scrambling and quantum chaos. We propose an efficient quantum algorithm to measure OTOCs that provides an exponential speed-up over the best known classical algorithm provided the OTOC operator to be estimated admits an efficient gate decomposition. We also discuss a scheme to obtain information about the eigenvalue spectrum and the spectral density of OTOCs.