Shadow process tomography of quantum channels

TL;DR

This paper extends shadow tomography techniques from quantum states to quantum channels, providing efficient algorithms and bounds for process characterization, significantly reducing measurement complexity in large quantum systems.

Contribution

It introduces shadow process tomography using the Choi isomorphism, offering rigorous bounds and algorithms for efficient quantum channel characterization.

Findings

Derived bounds on measurement complexity for process tomography

Developed algorithms for shadow process tomography

Enabled evaluation of channel concatenation and application to quantum states

Abstract

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scale exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.