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

• URL: http://arxiv.org/abs/2608.17846v1
• Date: Tue, 18 Aug 2026 14:43:22 GMT
• Title: Quantum Circuit for General Unitary: Improved T-count via Block Flattening and Dilation
• Abstract summary: We present a Clifford+$T$ quantum circuit construction that implements any classically specified unitary to within error $$.<n>The key innovation lies in treating the target unitary as a single block-encoded object rather than a long product of simpler operations.
• Score: 9.242453412591354
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $ε$ and achieves a worst-case $T$-count with leading exponential scaling of $2^{5n/4}$ whenever $\log(1/ε)=\operatorname{poly}(n)$. 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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