Quantum scrambling with classical shadows

TL;DR

This paper introduces protocols for measuring higher-point out-of-time-ordered correlators (OTOCs) using classical shadows, enabling efficient detection of quantum information scrambling in near-term quantum devices without complex operations.

Contribution

It proposes novel protocols for measuring higher-point OTOCs via classical shadow estimation, avoiding time-reversal and ancillary controls, suitable for near-term quantum hardware.

Findings

Protocols successfully measure higher-point OTOCs

Methods do not require time-reversal evolution

Applicable to near-term quantum devices

Abstract

Quantum dynamics is of fundamental interest and has implications in quantum information processing. The four-point out-of-time-ordered correlator (OTOC) is traditionally used to quantify quantum information scrambling under many-body dynamics. Due to the OTOC's unusual time ordering, its measurement is challenging. We propose higher-point OTOCs to reveal early-time scrambling behavior, and present protocols to measure any higher-point OTOC using the shadow estimation method. The protocols circumvent the need for time-reversal evolution and ancillary control. They can be implemented in near-term quantum devices with single-qubit readout.