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arXiv · 2312.03916

Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters

Dong An·Andrew M. Childs·Lin Lin
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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.

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Dong An, Andrew M. Childs, Lin Lin. 2023-12-06. Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters. https://doi.org/10.1007/s00220-025-05509-w

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