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.

翻译：学习复杂量子过程是量子计算与量子机器学习诸多领域的核心挑战，在量子基准测试、密码分析及变分量子算法中均有重要应用。本文首次提出了量子统计查询（QSQ）模型下研究量子过程学习的框架，并给出了面向量子过程的统计查询（QPSQs）的首个形式化定义。该框架使我们能够为任意量子过程提出高效的QPSQ学习器，并附带可证明的性能保证。我们还通过数值模拟验证了该算法的有效性。在该新框架中，我们证明了学习酉2-designs的指数级查询复杂度下界，以及学习哈达玛随机酉矩阵的双指数级下界。通过密码学应用实例，该框架的实践意义得以彰显：揭示了大规模经典读出量子物理不可克隆函数（CR-QPUFs）的漏洞，回应了量子硬件安全领域一个重要的开放性问题。本工作标志着理解量子过程可学习性及其安全含义的重要进展。