Improved Classical Shadow Tomography Using Quantum Computation

TL;DR

This paper presents an improved classical shadow tomography method that leverages quantum computation to exponentially reduce space complexity and quadratically enhance running time, enabling more efficient quantum state predictions.

Contribution

It introduces a novel CST procedure utilizing a quantum-to-classical-to-quantum process to optimize measurement and computation efficiency.

Findings

Exponential reduction in space complexity.

Quadratic improvement in running time.

Effective with Pauli measurements and Clifford circuits.

Abstract

Classical shadow tomography (CST) involves obtaining enough classical descriptions of an unknown state via quantum measurements to predict the outcome of a set of quantum observables. CST has numerous applications, particularly in algorithms that utilize quantum data for tasks such as learning, detection, and optimization. This paper introduces a new CST procedure that exponentially reduces the space complexity and quadratically improves the running time of CST with single-copy measurements. The approach utilizes a quantum-to-classical-to-quantum process to prepare quantum states that represent shadow snapshots, which can then be directly measured by the observables of interest. With that, calculating large matrix traces is avoided, resulting in improvements in running time and space complexity. The paper presents analyses of the proposed methods for CST, with Pauli measurements and Clifford circuits.