Tensor Decomposition for Non-Clifford Gate Minimization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918342807257088 |
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| author | Khoruzhii, Kirill Gelß, Patrick Pokutta, Sebastian |
| author_facet | Khoruzhii, Kirill Gelß, Patrick Pokutta, Sebastian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_15285 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tensor Decomposition for Non-Clifford Gate Minimization Khoruzhii, Kirill Gelß, Patrick Pokutta, Sebastian Quantum Physics Data Structures and Algorithms 68Q12 F.1.2; D.3.4; F.2.1 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. |
| title | Tensor Decomposition for Non-Clifford Gate Minimization |
| topic | Quantum Physics Data Structures and Algorithms 68Q12 F.1.2; D.3.4; F.2.1 |
| url | https://arxiv.org/abs/2602.15285 |