Optimal algorithms for materializing stabilizer states and Clifford gates from compact descriptions
Summarize this article with:
Quantum Physics arXiv:2604.15405 (quant-ph) [Submitted on 16 Apr 2026] Title:Optimal algorithms for materializing stabilizer states and Clifford gates from compact descriptions Authors:Hyunho Cha, Jungwoo Lee View a PDF of the paper titled Optimal algorithms for materializing stabilizer states and Clifford gates from compact descriptions, by Hyunho Cha and 1 other authors View PDF HTML (experimental) Abstract:Stabilizer states admit compact classical descriptions, but many downstream tasks still require their full amplitude vectors. Since the output itself has size $2^n$, the main algorithmic question is whether one can materialize an $n$-qubit stabilizer state vector in optimal $O(2^n)$ time, rather than paying an additional polynomial overhead. We answer this question in the affirmative. Starting from the standard quadratic-form representation of stabilizer states, we give an algorithm that runs in $O(2^n)$ time and $O(2^n)$ space. The idea is to maintain a cached parity word that records all future off-diagonal quadratic phase increments simultaneously. As consequences, we obtain an optimal procedure for materializing a stabilizer state vector from a standard check-matrix description, and an optimal algorithm for expanding a Clifford tableau into its full dense matrix. These results close the asymptotic gap for dense stabilizer and Clifford materialization. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.15405 [quant-ph] (or arXiv:2604.15405v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.15405 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hyunho Cha [view email] [v1] Thu, 16 Apr 2026 15:34:54 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal algorithms for materializing stabilizer states and Clifford gates from compact descriptions, by Hyunho Cha and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)