Gate-Efficient Implementation of the Query-Optimal Time-Dependent Hamiltonian Simulation
Abstract
The query-optimal algorithm of [CGWZ26] for general time-dependent Hamiltonian simulation uses q = O( αT + log(1/ε)/(log(e + log(1/ε)/(αT) )) ) queries to HAM−T within ε error for a Lipschitz-continuous time-dependent Hamiltonian H(t) on [0,T] satisfying lVert H(t)rVert≤α. However, its direct circuit implementation incurs a substantially larger gate overhead. In this note, we give an implementation of the same algorithm that retains its optimal query complexity and uses O[ q ( a + log(1 + (T(α+ βT))/ε ) ) ] one- and two-qubit gates, where a is the number of block-encoding ancilla qubits and β is the Lipschitz constant of H. The main ingredient is an exact dyadic factorization of the ordered update product in the underlying one-query transducer.
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BibTeX
@misc{chen2026gateefficient,
title = {{Gate-Efficient Implementation of the Query-Optimal Time-Dependent Hamiltonian Simulation}},
author = {Boyang Chen and Minbo Gao and Zhengfeng Ji and Tongyang Li and Xinzhao Wang and Shuo Zhou},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30629},
eprint = {2608.30629},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30629},
}
RIS
TY - UNPB
TI - Gate-Efficient Implementation of the Query-Optimal Time-Dependent Hamiltonian Simulation
AU - Boyang Chen
AU - Minbo Gao
AU - Zhengfeng Ji
AU - Tongyang Li
AU - Xinzhao Wang
AU - Shuo Zhou
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30629
UR - https://arxiv.org/abs/2608.30629
AB - The query-optimal algorithm of [CGWZ26] for general time-dependent Hamiltonian simulation uses q = O( αT + log(1/ε)/(log(e + log(1/ε)/(αT) )) ) queries to HAM−T within ε error for a Lipschitz-continuous time-dependent Hamiltonian H(t) on [0,T] satisfying lVert H(t)rVert≤α. However, its direct circuit implementation incurs a substantially larger gate overhead. In this note, we give an implementation of the same algorithm that retains its optimal query complexity and uses O[ q ( a + log(1 + (T(α+ βT))/ε ) ) ] one- and two-qubit gates, where a is the number of block-encoding ancilla qubits and β is the Lipschitz constant of H. The main ingredient is an exact dyadic factorization of the ordered update product in the underlying one-query transducer.
ER -