Quantum News
Sign In
Back to News
quantum-computing

Tensor Decomposition for Non-Clifford Gate Minimization

arXiv Quantum Physics
Loading...
3 min read
0 likes
⚡ Quantum Brief
Researchers introduced a novel algebraic method to minimize non-Clifford gates in quantum circuits, focusing on Toffoli gates instead of traditional T-count optimization. The approach leverages tensor decomposition over finite fields to reduce resource costs. The technique outperforms existing solutions, matching or improving benchmarks for both Toffoli and T-count minimization. Most circuits processed in under a minute on a single CPU, unlike prior work requiring thousands of TPUs. The method addresses fault-tolerant quantum computation’s key bottleneck: magic state distillation costs. By minimizing non-Clifford gates, it reduces overhead for error-corrected quantum algorithms. Authors connect Toffoli gate count to tensor rank over GF(2), enabling efficient algebraic optimization. This mathematical framework provides a scalable alternative to brute-force search methods. Published in February 2026, the work bridges quantum computing and algorithmic theory, offering practical gains for near-term fault-tolerant systems. Code and benchmarks are publicly accessible for validation.
Tensor Decomposition for Non-Clifford Gate Minimization

Summarize this article with:

ChatGPTChatGPTPerplexityPerplexityClaudeClaudeGrokGrok

Quantum Physics arXiv:2602.15285 (quant-ph) [Submitted on 17 Feb 2026] Title:Tensor Decomposition for Non-Clifford Gate Minimization Authors:Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta View a PDF of the paper titled Tensor Decomposition for Non-Clifford Gate Minimization, by Kirill Khoruzhii and 2 other authors View PDF HTML (experimental) Abstract:Fault-tolerant quantum computation requires minimizing non-Clifford gates, whose implementation via magic state distillation dominates the resource costs. While $T$-count minimization is well-studied, dedicated $CCZ$ factories shift the natural target to direct Toffoli minimization. We develop algebraic methods for this problem, building on a connection between Toffoli count and tensor decomposition over $\mathbb{F}_2$. On standard benchmarks, these methods match or improve all reported results for both Toffoli and $T$-count, with most circuits completing in under a minute on a single CPU instead of thousands of TPUs used by prior work. Subjects: Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS) MSC classes: 68Q12 ACM classes: F.1.2; D.3.4; F.2.1 Cite as: arXiv:2602.15285 [quant-ph] (or arXiv:2602.15285v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.15285 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kirill Khoruzhii [view email] [v1] Tue, 17 Feb 2026 01:11:07 UTC (851 KB) Full-text links: Access Paper: View a PDF of the paper titled Tensor Decomposition for Non-Clifford Gate Minimization, by Kirill Khoruzhii and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cs cs.DS 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)

Read Original

Source Information

Source: arXiv Quantum Physics