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.

翻译：从远程访问的量子计算与数据中进行量子学习必须解决两个关键挑战：验证数据的正确性，以及确保学习者的数据收集策略与所得结论的隐私性。Canetti 与 Karchmer（TCC 2021）提出的隐蔽（可验证）学习模型为经典学习算法提供了实现此类保证的框架。在本工作中，我们提出了量子学习理论中的隐蔽可验证学习模型，并在无需计算硬度假设的情况下，针对基于已确立量子数据优势的远程数据访问场景实现了这些模型。我们考虑两种隐私概念：（i）策略隐蔽性，即窃听者无法获取关于学习者策略的信息；（ii）目标隐蔽性，即窃听者无法获取关于待学习未知对象的信息。我们展示了：通过经典阴影进行量子统计查询的策略隐蔽算法；从公共量子样本与私有量子统计查询中学习二次函数的目标隐蔽算法，用于 Pauli 阴影层析与稳定子态学习（基于公共多副本与私有单副本量子测量），以及用于解决 Forrelation 问题与 Simon 问题（基于公共量子查询与私有经典查询），其中对手为单向或无关联辅助比特的独立同分布窃听者。特别地，最后一项结果证实了 Forrelation 问题与 Simon 问题中经典查询与量子查询之间的指数级分离在隐蔽性约束下依然成立。在此过程中，我们设计了从公共量子查询中获取量子数据的隐蔽可验证协议，这些协议可能具有独立的研究价值。总体而言，我们的模型及相应算法表明，即使面对不可信的远程数据，量子优势依然可以在私有且可验证的前提下实现。