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), while proving a secure instantiation of CR-QPUFs must exist. This addresses 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和量子机器学习中许多核心领域的挑战，其应用涵盖量子基准测试、密码分析以及变分量子算法。本文首次提出基于量子统计查询（QSQ）模型的研究框架，用于探索量子过程学习，并首次正式定义了对量子过程的统计查询（QPSQs）。该框架使我们能够提出一种高效的QPSQ学习器，适用于任意量子过程并具备可证明的性能保证。我们还提供了数值模拟以展示该算法的有效性。在新框架中，我们证明了学习酉2-设计的指数级查询复杂度下界，以及学习哈尔随机酉矩阵的双指数下界。该框架的实际意义通过密码学应用得以体现：揭示了大规模经典读出量子物理不可克隆函数（CR-QPUFs）的脆弱性，同时证明了安全的CR-QPUFs实例必然存在。这解决了量子硬件安全领域的一个关键开放问题。本工作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重要一步。