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Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
Dong An, Andrew M. Childs, Lin Lin·December 6, 2023·DOI: 10.1007/s00220-025-05509-w
Quantum Physicsmath.NA
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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.