Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

TL;DR

This paper introduces a method using classical shadow tomography to experimentally quantify quantum information scrambling on programmable quantum simulators, identifying signatures of chaos with minimal measurements.

Contribution

It develops shadow tomography protocols for time evolution channels and experimentally demonstrates signatures of quantum scrambling on a superconducting quantum processor.

Findings

Identified two signatures of quantum information scrambling.

Measured quantum chaos signatures in a superconducting quantum processor.

Validated results with numerical simulations.

Abstract

We develop techniques to probe the dynamics of quantum information, and implement them experimentally on an IBM superconducting quantum processor. Our protocols adapt shadow tomography for the study of time evolution channels rather than of quantum states, and rely only on single-qubit operations and measurements. We identify two unambiguous signatures of quantum information scrambling, neither of which can be mimicked by dissipative processes, and relate these to many-body teleportation. By realizing quantum chaotic dynamics in experiment, we measure both signatures, and support our results with numerical simulations of the quantum system. We additionally investigate operator growth under this dynamics, and observe behaviour characteristic of quantum chaos. As our methods require only a single quantum state at a time, they can be readily applied on a wide variety of quantum simulators.