Multi-Qubit Dyadic Phase Fixing for Fault-Tolerant Quantum Compilation
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Quantum Physics arXiv:2606.05397 (quant-ph) [Submitted on 3 Jun 2026] Title:Multi-Qubit Dyadic Phase Fixing for Fault-Tolerant Quantum Compilation Authors:Justin Kalloor, Mathias Weiden, Ed Younis, John Kubiatowicz, Costin Iancu View a PDF of the paper titled Multi-Qubit Dyadic Phase Fixing for Fault-Tolerant Quantum Compilation, by Justin Kalloor and 3 other authors View PDF HTML (experimental) Abstract:Fault-tolerant quantum computing requires translating application-level quantum circuits into the Clifford+$T$ gate set, where the $T$ gate is the dominant resource cost. Phase kickback is an ancilla-based technique that can dramatically reduce $T$-count for rotations with dyadic angles, but has previously been limited to highly structured circuit families. We present Dyadic Phase Fixing (DPF), a general multi-qubit synthesis tool that extends phase kickback to general quantum circuits. DPF uses numerical unitary synthesis to greedily extract dyadic angle rotations from any input circuit. Combined with a decision matrix to automatically size the final phase gradient register, our end-to-end workflow achieves up to 70% reduction in $T$-count compared to \texttt{gridsynth} and up to 60% compared to Repeat-Until-Success synthesis on a diverse set of benchmarks. We map these compiled circuits to a surface-code architecture to evaluate space-time volume, demonstrating up to a 60\% reduction in this metric as well. However, for some circuits and mapping strategies the two metrics diverge significantly, demonstrating that $T$-count alone is a useful but incomplete proxy for fault-tolerant program costs. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.05397 [quant-ph] (or arXiv:2606.05397v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.05397 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Justin Kalloor [view email] [v1] Wed, 3 Jun 2026 20:07:30 UTC (1,978 KB) Full-text links: Access Paper: View a PDF of the paper titled Multi-Qubit Dyadic Phase Fixing for Fault-Tolerant Quantum Compilation, by Justin Kalloor and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)