Learning Quantum Processes with Quantum Statistical Queries

TL;DR

This paper introduces a new model for learning quantum processes using quantum statistical queries, providing algorithms and bounds for shadow and process tomography, with applications in quantum security.

Contribution

It pioneers the study of quantum process learning via quantum statistical queries, offering algorithms, bounds, and practical security applications.

Findings

Efficient average-case shadow tomography algorithm.

Lower bounds for learning unitaries, including exponential for 2-designs.

Application to quantum hardware security protocols.

Abstract

In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with respect to diamond distance. For the former, we present an efficient average-case algorithm along with a nearly matching lower bound with respect to the number of observables to be predicted. For the latter, we present average-case query complexity lower bounds for learning classes of unitaries. We obtain an exponential lower bound for learning unitary 2-designs and a doubly exponential lower bound for Haar-random unitaries. Finally, we demonstrate the practical relevance of our access model by applying our learning algorithm to attack an authentication protocol using Classical-Readout Quantum Physically Unclonable Functions, partially addressing an important open question in quantum hardware security.