Proposal for measuring out-of-time-ordered correlators at finite temperature with coupled spin chains

TL;DR

This paper proposes a practical protocol to measure out-of-time-ordered correlators at finite temperature in spin chains, addressing experimental challenges and error mitigation for quantum information scrambling studies.

Contribution

It introduces a method to measure finite-temperature OTOCs in coupled spin chains without sign-reversal, including error mitigation and robustness to decoherence.

Findings

Protocol successfully measures OTOC without sign-reversal

Error mitigation techniques improve measurement accuracy

Method is robust against typical experimental decoherence

Abstract

Information scrambling, which is the spread of local information through a system's many-body degrees of freedom, is an intrinsic feature of many-body dynamics. In quantum systems, the out-of-time-ordered correlator (OTOC) quantifies information scrambling. Motivated by experiments that have measured the OTOC at infinite temperature and a theory proposal to measure the OTOC at finite temperature using the thermofield double state, we describe a protocol to measure the OTOC in a finite temperature spin chain that is realized approximately as one half of the ground state of two moderately-sized coupled spin chains. We consider a spin Hamiltonian with particle-hole symmetry, for which we show that the OTOC can be measured without needing sign-reversal of the Hamiltonian. We describe a protocol to mitigate errors in the estimated OTOC, arising from the finite approximation of the system to the thermofield double state. We show that our protocol is also robust to main sources of decoherence in experiments.