T-efficient unitary synthesis via block-sparse Hamiltonian simulation
Abstract
We construct Clifford+T circuits implementing arbitrary n-qubit unitaries with worst-case T-count Õ(N8/7) at constant operator-norm error, where N=2n, improving the previous exponent 5/4. The construction uses Õ(N6/7) clean ancillas. The main idea is to reduce the data addressed by each query to the block-encoding circuit for a sparse piece while controlling the additional simulation work needed to combine the pieces. We simulate a Hermitian logarithm of the target by flattening its traceless part with a two-layer random similarity transformation, randomly partitioning the transformed generator into block-sparse Hermitian pieces, and combining their evolutions using qDRIFT. For a target operator-norm error ε∈(0,1/2), let L=log2(N/ε), the qubit count plus the requested bits of accuracy. By successively correcting the approximation error, we obtain a circuit using Õ(N8/7L3/7+NL) T gates and Õ(N) clean ancillas whenever L≤ N. We also prove that, at constant precision, the exponent 8/7 is optimal within a sequential block-SELECT model.
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BibTeX
@misc{liu2026tefficient,
title = {{$T$-efficient unitary synthesis via block-sparse Hamiltonian simulation}},
author = {Diyi Liu and Shuchen Zhu and Wibe Albert de Jong and Di Fang and David Williams-Young and Chao Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18589},
eprint = {2610.18589},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18589},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - T-efficient unitary synthesis via block-sparse Hamiltonian simulation
AU - Diyi Liu
AU - Shuchen Zhu
AU - Wibe Albert de Jong
AU - Di Fang
AU - David Williams-Young
AU - Chao Yang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18589
UR - https://arxiv.org/abs/2610.18589
AB - We construct Clifford+T circuits implementing arbitrary n-qubit unitaries with worst-case T-count Õ(N^8/7) at constant operator-norm error, where N=2^n, improving the previous exponent 5/4. The construction uses Õ(N^6/7) clean ancillas. The main idea is to reduce the data addressed by each query to the block-encoding circuit for a sparse piece while controlling the additional simulation work needed to combine the pieces. We simulate a Hermitian logarithm of the target by flattening its traceless part with a two-layer random similarity transformation, randomly partitioning the transformed generator into block-sparse Hermitian pieces, and combining their evolutions using qDRIFT. For a target operator-norm error ε∈(0,1/2), let L=log_2(N/ε), the qubit count plus the requested bits of accuracy. By successively correcting the approximation error, we obtain a circuit using Õ(N^8/7L^3/7+NL) T gates and Õ(N) clean ancillas whenever L≤ N. We also prove that, at constant precision, the exponent 8/7 is optimal within a sequential block-SELECT model.
ER -