Diagnosis of information scrambling from Hamiltonian evolution under decoherence

TL;DR

This paper introduces a quantum teleportation protocol to diagnose information scrambling in noisy quantum systems, demonstrating its effectiveness on spin chains and lattice Yang-Mills theories through numerical simulations.

Contribution

It proposes a decoherence-resilient method for diagnosing quantum information scrambling using a teleportation-based protocol applied to complex physical models.

Findings

Yang-Mills-Ising model exhibits late-time scrambling signals

Protocol effectively detects scrambling despite decoherence

Numerical simulation demonstrates practical applicability

Abstract

We apply a quantum teleportation protocol based on the Hayden-Preskill thought experiment to quantify how scrambling a given quantum evolution is. It has an advantage over the direct measurement of out-of-time ordered correlators when used to diagnose the information scrambling in the presence of decoherence effects stemming from a noisy quantum device. We demonstrate the protocol by applying it to two physical systems: Ising spin chain and SU(2) lattice Yang-Mills theory. To this end, we numerically simulate the time evolution of the two theories in the Hamiltonian formalism. The lattice Yang-Mills theory is implemented with a suitable truncation of Hilbert space on the basis of the Kogut-Susskind formalism. On a two-leg ladder geometry and with the lowest nontrivial spin representations, it can be mapped to a spin chain, which we call it Yang-Mills-Ising model and is also directly applicable to future digital quantum simulations. We find that the Yang-Mills-Ising model shows the signal of information scrambling at late times.