Quantum Representation Learning Beyond Pairwise Fidelity
Abstract
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.
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BibTeX
@misc{hou2026quantum,
title = {{Quantum Representation Learning Beyond Pairwise Fidelity}},
author = {Junpeng Hou and Changbin Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01797},
eprint = {2609.01797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01797},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Representation Learning Beyond Pairwise Fidelity
AU - Junpeng Hou
AU - Changbin Lu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01797
UR - https://arxiv.org/abs/2609.01797
AB - 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.
ER -