Stabilizers for Compiling Logical Circuits under Hardware Constraints
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Quantum Physics arXiv:2604.25042 (quant-ph) [Submitted on 27 Apr 2026] Title:Stabilizers for Compiling Logical Circuits under Hardware Constraints Authors:Jack Weinberg, Narayanan Rengaswamy View a PDF of the paper titled Stabilizers for Compiling Logical Circuits under Hardware Constraints, by Jack Weinberg and Narayanan Rengaswamy View PDF HTML (experimental) Abstract:To implement quantum algorithms on a quantum computer, we must overcome the twin problems of fault-tolerance -- how can we realize a relatively noiseless computation by cleverly combining noisy components? -- and compilation -- how can we realize an arbitrary quantum algorithm given the basic operations available on the quantum device at hand? We show how treating the former problem via error-correcting codes enables greater flexibility in resolving the latter. Specifically, we explicitly leverage the fact that error-correcting codes introduce redundancy which renders physically distinct operators logically indistinguishable. In terms of computation, it suffices to implement any operator logically equivalent to some target, yet from a compilation perspective, certain choices may be preferable to others. Our novel contribution is making this intuition precise in the general setting of the special unitary group. In particular, we describe how to reduce the problem of making a compilation-ideal choice to a least squares problem and provide a closed form solution thereof. Using our framework, it is possible to circumvent inserting costly swaps to adhere to hardware connectivity; instead, we could realize the logical target through a distinct physical Hamiltonian that is natively accessible. We elucidate our approach using the $[[4,2,2]]$ code. We discuss connections to compressed sensing that may pave the way to efficient compilation leveraging physical degrees of freedom. Comments: Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2604.25042 [quant-ph] (or arXiv:2604.25042v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.25042 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jack Weinberg [view email] [v1] Mon, 27 Apr 2026 22:48:46 UTC (35 KB) Full-text links: Access Paper: View a PDF of the paper titled Stabilizers for Compiling Logical Circuits under Hardware Constraints, by Jack Weinberg and Narayanan RengaswamyView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cs cs.IT math math.IT 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?)