🤖 AI Summary
This work addresses quantum process learning by introducing the Quantum Process Statistical Query (QPSQ) model—the first statistical query framework tailored to quantum processes. Methodologically, it formalizes the QPSQ oracle access model, designs provably efficient shadow tomography and diamond-norm tomography algorithms, and rigorously establishes learning lower bounds—ranging from exponential to doubly exponential—for 2-design and Haar-random unitary processes via complexity-theoretic analysis and numerical simulation. Key contributions are: (1) establishing the theoretical foundations and learnability limits of the QPSQ model; (2) exposing critical security vulnerabilities in classical-readout quantum physical unclonable functions (CR-QPUFs), successfully breaking their authentication protocols; and (3) delivering a quantum process learning paradigm that simultaneously achieves strong theoretical guarantees and practical feasibility.
📝 Abstract
Learning complex quantum processes is a central challenge in many areas of quantum computing and quantum machine learning, with applications in quantum benchmarking, cryptanalysis, and variational quantum algorithms. This paper introduces the first learning framework for studying quantum process learning within the Quantum Statistical Query (QSQ) model, providing the first formal definition of statistical queries to quantum processes (QPSQs). The framework allows us to propose an efficient QPSQ learner for arbitrary quantum processes accompanied by a provable performance guarantee. We also provide numerical simulations to demonstrate the efficacy of this algorithm. In our new framework, we prove exponential query complexity lower bounds for learning unitary 2-designs, and a doubly exponential lower bound for learning haar-random unitaries. The practical relevance of this framework is exemplified through application in cryptography, highlighting vulnerabilities of a large class of Classical-Readout Quantum Physical Unclonable Functions (CR-QPUFs), addressing an important open question in the field of quantum hardware security. This work marks a significant step towards understanding the learnability of quantum processes and shedding light on their security implications.
