Multi-Qubit Dyadic Phase Fixing for Fault-Tolerant Quantum Compilation

Quantum Physics [Submitted on 3 Jun 2026] Multi-Qubit Dyadic Phase Fixing for Fault-Tolerant Quantum Compilation Justin Kalloor, Mathias Weiden, Ed Younis, John Kubiatowicz, Costin Iancu 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 Submission history From: Justin Kalloor [view email] [v1] Wed, 3 Jun 2026 20:07:30 UTC (1,978 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)