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 ε and achieves a worst-case T-count with leading exponential scaling of 25n/4 whenever log(1/ε)=poly(n). This improves upon the best previous 24n/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.
Related
- Optimal Quantum-Circuit Synthesis and Implementation of General Unitaries with Parallelized Bitstring-Conditioned Rotations
- General circuit mapping algorithm for neutral atom quantum computers
- SMP: A General Hyperedge-Based Framework for Circuit-Level Quantum Error Correction
- General Quantum Circuit Framework for Extended Wigner’s Friend Scenarios: Logically and Causally Consistent Reasoning without Absolute Measurement Events
- Interaction induced flattening of optical transition quantum geometry
BibTeX
@misc{yuan2026quantum,
title = {{Quantum Circuit for General Unitary: Improved T-count via Block Flattening and Dilation}},
author = {Pei Yuan and Shengyu Zhang and Wei Zi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.17846},
eprint = {2608.17846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17846},
}
RIS
TY - UNPB
TI - Quantum Circuit for General Unitary: Improved T-count via Block Flattening and Dilation
AU - Pei Yuan
AU - Shengyu Zhang
AU - Wei Zi
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.17846
UR - https://arxiv.org/abs/2608.17846
AB - 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)=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.
ER -