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arXiv · 2608.17846

Quantum Circuit for General Unitary: Improved T-count via Block Flattening and Dilation

Pei Yuan·Shengyu Zhang·Wei Zi
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Abstract

Synthesizing arbitrary $n$-qubit unitaries using as few non-Clifford gates as possible is a central problem in fault-tolerant quantum compilation. We present a Clifford+$T$ quantum circuit construction that approximately implements any classically specified unitary to within error $\epsilon$ and achieves a worst-case $T$-count with leading exponential scaling of $2^{5n/4}$ whenever $\log(1/\epsilon)=\operatorname{poly}(n)$. This improves upon the best previous $2^{4n/3}$ scaling. The key innovation lies in treating the target unitary as a single block-encoded object rather than a long product of simpler operations. A technique of block flattening controls the normalization while preserving an efficient implementation of the block encoding; subsequently, quantum singular value transformation maps its common singular value to one, thereby recovering the target unitary.

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Pei Yuan, Shengyu Zhang, Wei Zi. 2026-08-18. Quantum Circuit for General Unitary: Improved T-count via Block Flattening and Dilation. https://arxiv.org/abs/2608.17846

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