Quantum Parity Representations: Learnable Basis Discovery, Encoders, and Shadow Deployment
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Quantum Physics arXiv:2605.11213 (quant-ph) [Submitted on 11 May 2026] Title:Quantum Parity Representations: Learnable Basis Discovery, Encoders, and Shadow Deployment Authors:Sang Hyub Kim, Oliver Knitter, Jonathan Mei, Claudio Girotto, Masako Yamada, Martin Roetteler, Chi Chen (IonQ Inc.) View a PDF of the paper titled Quantum Parity Representations: Learnable Basis Discovery, Encoders, and Shadow Deployment, by Sang Hyub Kim and 6 other authors View PDF HTML (experimental) Abstract:We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or when discrete inference interfaces support perturbation robustness. A parity feature is a signed product over selected bits of a binary input: once the participating bits are known, evaluation requires no quantum resources. Reaching a useful parity representation requires solving two challenges. When the input is parity-ready (a meaningful binary string), the challenge is basis discovery: selecting useful parity words from a combinatorial search space. Otherwise, the challenge is encoding: constructing a binary vector on which parity computation is meaningful. We use hybrid quantum-classical training pipelines to address these: learnable Pauli word selection for basis discovery, learned projection encodings for continuous embeddings, and sPQC-Parity for discrete inputs. On three native-binary parity tasks with 5-10 qubits, the learned parity basis improves mean accuracy by 23.9% to 41.7% over logistic-regression and support-vector baselines. A model comparison shows that the improvement comes primarily from discovering the right parity basis, rather than from quantum moment computation at inference. On five continuous text benchmarks, learned projection recovers much of the loss introduced by dimensionality reduction and fixed binarization, exceeding the full continuous baseline on CR, SST-2, and SST-5. On three encoding-limited discrete datasets, when compared with PCA-bin as the baseline, sPQC-Parity reaches 94.6% improvement on mushroom, 3.0% on splice, and matches PCA-bin on promoter. We also analyze inference robustness under binary or quantized inference, where rounding gives exact invariance below half the quantization step. Comments: Subjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET) Cite as: arXiv:2605.11213 [quant-ph] (or arXiv:2605.11213v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.11213 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sang Hyub Kim [view email] [v1] Mon, 11 May 2026 20:28:03 UTC (46 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Parity Representations: Learnable Basis Discovery, Encoders, and Shadow Deployment, by Sang Hyub Kim and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cs cs.ET References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)