Plateau-Constrained Selection of Commuting Phase-Term Orderings Under a Fixed Maintained-Parity Compiler Contract

[2608.27592] Plateau-Constrained Selection: Exploiting Degeneracy for Lower-Depth Quantum Compilation Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2608.27592 (quant-ph) [Submitted on 27 Aug 2026 ( v1 ), last revised 11 Sep 2026 (this version, v2)] Title: Plateau-Constrained Selection: Exploiting Degeneracy for Lower-Depth Quantum Compilation Authors: Owen Friedewald , Ali Shiri Sichani , Chi-Ren Shyu View PDF HTML (experimental) Abstract: Minimum-cost orders of commuting phase terms can produce substantially different routed circuits. On the same 36-term instances, three orders with identical support cost 74 yield mean routed depths of 228.6, 233.8, and 256.7. We exploit this degeneracy under fixed placement and maintained-parity lowering: Stage 1 attains the support optimum, and Stage 2 selects minimum routed depth among 24 equal-cost orders. For distinct pair supports, we characterize orders attaining the support lower bound through Hamiltonian paths of the support line graph and count optima exactly through 20 terms. On synthetic 16-qubit assignment-Ising instances, selection reduces depth by 12.83% under a different SABRE routing seed, with lower depth in all 20 instances. The selected orders lie a median 1.57 pool standard deviations below the pool mean, consistent with ordinary best-of-24 selection; the useful feature is that candidate rankings persist across routing seeds. Depth reductions extend to 48 terms and a random-MaxCut generator, whereas evaluation with BasicSwap reverses the gain. A 40-instance IBM Heron study measures a 0.59% error reduction on the executed stabilizer-probe panel, but the primary confidence interval across instances includes zero. Plateau selection therefore improves routed depth in the tested SABRE pipeline while preserving the logical support optimum. Comments: 11 pages, 4 figures. Under review at IEEE Transactions on Quantum Engineering Subjects: Quantum Physics (quant-ph) ; Emerging Technologies (cs.ET) Cite as: arXiv:2608.27592 [quant-ph] (or arXiv:2608.27592v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.27592 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Owen Friedewald [ view email ] [v1] Thu, 27 Aug 2026 18:22:15 UTC (318 KB) [v2] Fri, 11 Sep 2026 18:20:37 UTC (146 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-08 Change to browse by: cs cs.ET 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 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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