Probing quantum information propagation with out-of-time-ordered correlators

TL;DR

This paper demonstrates the measurement of out-of-time-ordered correlators (OTOCs) in a 2D quantum system using superconducting circuits, revealing insights into quantum information propagation, thermalization, and localization phenomena.

Contribution

It introduces an experimental method to measure OTOCs in a 2D lattice, enabling study of quantum information dynamics and many-body localization with superconducting circuits.

Findings

Successfully measured OTOCs in a 2D Bose-Hubbard lattice

Observed partial overcoming of localization with increased particles

Demonstrated coherent time-reversal using digital-analog simulation

Abstract

Interacting many-body quantum systems show a rich array of physical phenomena and dynamical properties, but are notoriously difficult to study: they are challenging analytically and exponentially difficult to simulate on classical computers. Small-scale quantum information processors hold the promise to efficiently emulate these systems, but characterizing their dynamics is experimentally challenging, requiring probes beyond simple correlation functions and multi-body tomographic methods. Here, we demonstrate the measurement of out-of-time-ordered correlators (OTOCs), one of the most effective tools for studying quantum system evolution and processes like quantum thermalization. We implement a 3x3 two-dimensional hard-core Bose-Hubbard lattice with a superconducting circuit, study its time-reversibility by performing a Loschmidt echo, and measure OTOCs that enable us to observe the propagation of quantum information. A central requirement for our experiments is the ability to coherently reverse time evolution, which we achieve with a digital-analog simulation scheme. In the presence of frequency disorder, we observe that localization can partially be overcome with more particles present, a possible signature of many-body localization in two dimensions.