Optimal algorithms for materializing stabilizer states and Clifford gates from compact descriptions

Quantum Physics [Submitted on 16 Apr 2026] Optimal algorithms for materializing stabilizer states and Clifford gates from compact descriptions Hyunho Cha, Jungwoo Lee 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: 16 pages 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 Submission history From: Hyunho Cha [view email] [v1] Thu, 16 Apr 2026 15:34:54 UTC (14 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)