PreprintarXiv licencearXiv
Optimal Linear Combination of Hamiltonian Simulation for Dissipative Dynamics
Abstract
Linear combination of Hamiltonian simulation (LCHS) is an efficient method for simulating dissipative dynamics on quantum computers. The choice of the LCHS kernel controls the cost of the algorithm. We prove that the kernel family proposed by Ni and Ying~\cite{NY26} minimizes the LCHS query cost in the minimax sense. For target accuracy ε, the minimum cost is asymptotically 2e/π(ln1/ε−lnln1/ε+o(1)), with optimal leading constant 2e/π. Our lower-bound proof combines weak duality with a realization lemma that approximates extremal dual functions by matrix elements of dissipative evolutions.
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BibTeX
@misc{ni2026optimal,
title = {{Optimal Linear Combination of Hamiltonian Simulation for Dissipative Dynamics}},
author = {Hongkang Ni and Lexing Ying},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39541},
eprint = {2610.39541},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39541},
}
RIS
TY - UNPB
TI - Optimal Linear Combination of Hamiltonian Simulation for Dissipative Dynamics
AU - Hongkang Ni
AU - Lexing Ying
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39541
UR - https://arxiv.org/abs/2610.39541
AB - Linear combination of Hamiltonian simulation (LCHS) is an efficient method for simulating dissipative dynamics on quantum computers. The choice of the LCHS kernel controls the cost of the algorithm. We prove that the kernel family proposed by Ni and Ying~\cite{NY26} minimizes the LCHS query cost in the minimax sense. For target accuracy ε, the minimum cost is asymptotically 2e/π(ln1/ε−lnln1/ε+o(1)), with optimal leading constant 2e/π. Our lower-bound proof combines weak duality with a realization lemma that approximates extremal dual functions by matrix elements of dissipative evolutions.
ER -