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. The practical relevance of this framework is exemplified through application in cryptanalysis, highlighting vulnerabilities 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、密码分析和变分量子算法中具有重要应用。本文首次提出了基于量子统计查询（QSQ）模型的量子过程学习框架，正式定义了针对量子过程的统计查询（QPSQs）。该框架支持我们提出一种具有可证明性能保证的高效QPSQ学习器，适用于任意量子过程。我们还通过数值模拟验证了该算法的有效性。通过将其应用于密码分析，该框架的实际意义得到充分体现——我们揭示了经典读出型量子物理不可克隆函数（CR-QPUFs）的脆弱性，解答了量子硬件安全领域一个重要的开放性问题。本研究标志着在理解量子过程可学习性及其安全影响方面迈出了关键一步。