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

2023/12/06 by An, Dong, Childs, Andrew M., Lin, Lin · 28 citations
#FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2312.03916

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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