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Paper 1
Tensor Decomposition for Non-Clifford Gate Minimization
Kirill Khoruzhii, Patrick Gelß, Sebastian Pokutta
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2602.15285
- arXiv
- 2602.15285
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.
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