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arXiv · 2509.25702

Unitary synthesis with fewer T gates

Xinyu Tan
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Abstract

We present a simple algorithm that implements an arbitrary $n$-qubit unitary operator using a Clifford+T circuit with T-count $O(2^{4n/3} n^{2/3})$. This improves upon the previous best known upper bound of $O(2^{3n/2} n)$, while the best known lower bound remains $\Omega(2^n)$. Our construction is based on a recursive application of the cosine-sine decomposition, together with a generalization of the optimal diagonal unitary synthesis method by Gosset, Kothari, and Wu to multi-controlled $k$-qubit unitaries.

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Xinyu Tan. 2025-09-30. Unitary synthesis with fewer T gates. https://arxiv.org/abs/2509.25702

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