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Quantum Simulation
Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
arXiv
Authors: Dong An, Andrew M. Childs, Lin Lin
Year
2023
Paper ID
52774
Status
Preprint
Abstract Read
~2 min
Abstract Words
81
Citations
N/A
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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- 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...
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