Learning Quantum Processes with Quantum Statistical Queries
This work addresses foundational challenges in quantum machine learning and security, offering new theoretical insights and practical implications for quantum hardware authentication.
The paper tackles the problem of learning quantum processes using quantum statistical queries, presenting efficient algorithms for shadow tomography and establishing exponential lower bounds for process tomography of unitaries, with practical application to attacking a quantum hardware security protocol.
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.