Error-resilient Reversal of Quantum Chaotic Dynamics Enabled by Scramblons

TL;DR

This paper demonstrates a method to reverse quantum chaotic dynamics in many-body systems by using scramblon theory to mitigate errors, enabling measurement of quantum chaos indicators like the Lyapunov exponent.

Contribution

It introduces a novel protocol leveraging scramblon theory to accurately reverse quantum many-body dynamics and measure chaos indicators in solid-state NMR experiments.

Findings

Validated scramblon theory predictions with experimental data

Successfully isolated and mitigated errors in OTOC measurements

First experimental extraction of quantum Lyapunov exponent in a many-body system

Abstract

The emergence of the arrow of time in quantum many-body systems stems from the inherent tendency of Hamiltonian evolution to scramble quantum information and increase entanglement. While, in principle, one might counteract this temporal directionality by engineering a perfectly inverted Hamiltonian to reverse entanglement growth, such a scenario is fundamentally unstable because even minor imperfections in the backward evolution can be exponentially amplified, a hallmark of quantum many-body chaos. Therefore, successfully reversing quantum many-body dynamics demands a deep understanding of the underlying structure of quantum information scrambling and chaotic dynamics. In this letter, by using solid-state nuclear magnetic resonance on a macroscopic ensemble of randomly interacting spins, we measure the out-of-time-ordered correlator (OTOC) and validate key predictions of scramblon theory, a universal theoretical framework for information scrambling. Crucially, this theory enables us to isolate and mitigate errors in the OTOC caused by imperfections in the backward evolution. As a result, this protocol uncovers the anticipated exponential behavior of quantum many-body chaos and extracts the quantum Lyapunov exponent in a many-body experimental system for the first time. Our results push the fundamental limits of dynamical reversibility of complex quantum systems, with implications for quantum simulation and metrology.