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

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.

arXiv:2608.17846 [quant-ph]

(or arXiv:2608.17846v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.17846 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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