Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
Quantum Physics
2025-12-16 v2 Numerical Analysis
Numerical Analysis
Abstract
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.
Cite
@article{arxiv.2312.03916,
title = {Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters},
author = {Dong An and Andrew M. Childs and Lin Lin},
journal= {arXiv preprint arXiv:2312.03916},
year = {2025}
}
Comments
Published version with newly added Section 4.4.4, updated Appendix F, and improved presentation