Out-of-time-order correlators in electronic structure using Quantum Computers

TL;DR

This paper investigates operator spreading in quantum simulations of electronic structures using quantum computers, revealing how out-of-time-order correlators behave in different geometries and their relation to entanglement dynamics.

Contribution

It demonstrates the application of OTOCs to electronic structure simulations on quantum computers, highlighting the effects of geometry and entanglement on operator spreading.

Findings

Operator spreading is enhanced far from equilibrium.

Distinct area- and volume-law signatures in entanglement dynamics.

Results are experimentally implementable on current quantum platforms.

Abstract

Operator spreading has profound implications in diverse fields ranging from statistical mechanics and blackhole physics to quantum information. The usual way to quantify it is through out-of-time-order correlators (OTOCs), which are the quantum analog to Lyapunov exponents in classical chaotic dynamics. In this work we explore the phenomenon of operator spreading in quantum simulation of electronic structure in quantum computers. To substantiate our results, we focus on a hydrogen chain $H_4$ and demonstrate that operator spreading is enhanced when the chain is far from its equilibrium geometry. We also investigate the dynamics of bipartite entanglement and its dependence on the partition's size. Our findings reveal distinctive signatures closely resembling area- and volume-laws in equilibrium and far-from-equilibrium geometries, respectively. Our results provide insight of operator spreading of coherent errors in quantum simulation of electronic structure and can be experimentally implemented in various platforms available today.