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arXiv · 2607.12907

Unitary Synthesis with Near-Optimal T-Count for Near-Clifford Unitaries

Wang Fang·Chris Heunen·Qisheng Wang
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Abstract

We present an approach to unitary synthesis that implements an arbitrary $n$-qubit unitary operator $U$ by a Clifford+T circuit with T-count $\widetilde{O}(2^n d_F^{\mathcal{C}}(U))$, where $d_F^{\mathcal{C}}(U)$ is the Frobenius norm distance of $U$ to the Clifford group. The T-count is shown to be near-optimal when $d_F^{\mathcal{C}}(U)$ is a constant. Our approach improves the previous best upper bound $\widetilde{O}(2^{4n/3})$ due to Tan (2025) for a large class of unitary operators $U$ as long as $d_F^{\mathcal{C}}(U) \ll 2^{n/3}$.

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Wang Fang, Chris Heunen, Qisheng Wang. 2026-07-14. Unitary Synthesis with Near-Optimal T-Count for Near-Clifford Unitaries. https://arxiv.org/abs/2607.12907

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