超越两两保真度的量子表示学习

中文摘要 AI 辅助

量子对比学习、度量学习和自监督学习通常通过转移概率（尤其是保真度）向学习器暴露编码后的量子态。已知量子态具有高阶关系不变量，但它们对学习到的表示的影响仍不清楚。本文表明，仅使用转移概率的学习界面在某些量子态族中可能存在精确的连续盲方向。我们通过由相干重叠振幅和负掩码构建的批量算子恢复此缺失信息，其中其二阶矩$q_-$保留四态干涉。此外，$q_-$可通过双副本干涉直接测量，并可通过参数移位等方法进入变分学习。在来自拓扑码和双半子态的关系四元组中，该保真度盲信号编码了不等价的模数据，尽管两两保真度相同。最后，在存在制备漂移的四光子基准测试中，在相同总采样预算下，用对应的归一化$q_-$增强两个正交探针处的所有六个两两保真度，将分布外平均相位误差降低了86%。这些结果确立了多态关系可观测量作为可测量、可训练且具有物理意义的信号，用于超越两两保真度的量子表示学习。

英文摘要

Quantum contrastive, metric, and self-supervised learning often expose encoded quantum states to the learner through transition probabilities, especially fidelity. Quantum states are known to possess higher-order relational invariants, but their consequences for learned representations remain unclear. Here we show that a transition-probability-only learning interface can possess exact continuous blind directions in certain quantum-state families. We recover this missing information with a batch operator, built from coherent overlap amplitudes and negative masking, where its second moment $q_-$ retains four-state interference. Moreover, $q_-$ is directly measurable through two-copy interference and can enter variational learning via methods like parameter shift. In relational quartets derived from toric-code and double-semion states, this fidelity-blind signal encodes inequivalent modular data despite identical pairwise fidelities. Finally, in a four-photon benchmark with preparation drift, augmenting all six pairwise fidelities at two orthogonal probes with the corresponding normalized $q_-$ reduces the mean out-of-distribution phase error by $86\%$ at equal total shot budget. These results establish multistate relational observables as measurable, trainable, and physically consequential signals for quantum representation learning beyond pairwise fidelity.

发表机构

• Pinterest Inc.（Pinterest公司）
• Washington University in St. Louis（华盛顿大学圣路易斯分校）
• Anhui University of Technology（安徽工业大学）

机构由 AI 辅助整理，请以论文原文为准。

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19 pages, 4 figures