arXiv:2510.07193quant-phcs.CR2025-10

让量子学习在不泄露策略和结论的前提下,安全验证远程数据的正确性。

Covert Quantum Learning: Privately and Verifiably Learning from Quantum Data

  • 用经典阴影实现隐蔽的量子统计查询,保护学习策略
  • 在公开量子数据下学习二次函数、稳定态等,保持目标隐私
  • 证明量子查询优势在隐蔽条件下仍成立,适合安全量子计算场景

从远程访问的量子计算与数据中进行量子学习,需同时解决数据正确性验证与学习者策略及结论隐私保护问题。本文将经典隐蔽可验证学习模型拓展至量子学习理论,在无需计算难题假设的远程数据场景下实现该目标。提出两种隐私定义:(i) 策略隐蔽性——窃听者无法获知学习策略;(ii) 目标隐蔽性——窃听者无法获知待学习对象。我们展示了:通过经典阴影实现策略隐蔽的量子统计查询;在公开量子样本与私有量子统计查询下,实现二次函数、泡利阴影量子态层析与稳定态学习,以及从公开量子查询与私有经典查询中求解Forrelation和Simon问题的隐蔽算法。其中,敌手为单向或独立同分布、无辅助量子比特的窃听者。特别地,结果表明Forrelation和Simon问题中经典与量子查询的指数级差距在隐蔽约束下依然存在。此外,设计了基于公开量子查询的隐蔽可验证量子数据获取协议,可能具有独立意义。整体表明,即使面对不可信远程数据,量子优势也可在隐私与可验证前提下实现。

原文摘要 · Abstract (English)

Quantum learning from remotely accessed quantum compute and data must address two key challenges: verifying the correctness of data and ensuring the privacy of the learner's data-collection strategies and resulting conclusions. The covert (verifiable) learning model of Canetti and Karchmer (TCC 2021) provides a framework for endowing classical learning algorithms with such guarantees. In this work, we propose models of covert verifiable learning in quantum learning theory and realize them without computational hardness assumptions for remote data access scenarios motivated by established quantum data advantages. We consider two privacy notions: (i) strategy-covertness, where the eavesdropper does not gain information about the learner's strategy; and (ii) target-covertness, where the eavesdropper does not gain information about the unknown object being learned. We show: Strategy-covert algorithms for making quantum statistical queries via classical shadows; Target-covert algorithms for learning quadratic functions from public quantum examples and private quantum statistical queries, for Pauli shadow tomography and stabilizer state learning from public multi-copy and private single-copy quantum measurements, and for solving Forrelation and Simon's problem from public quantum queries and private classical queries, where the adversary is a unidirectional or i.i.d. ancilla-free eavesdropper. The lattermost results in particular establish that the exponential separation between classical and quantum queries for Forrelation and Simon's problem survives under covertness constraints. Along the way, we design covert verifiable protocols for quantum data acquisition from public quantum queries which may be of independent interest. Overall, our models and corresponding algorithms demonstrate that quantum advantages are privately and verifiably achievable even with untrusted, remote data.

量子学习隐私保护可验证量子优势

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