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

• URL: http://arxiv.org/abs/2312.03916v1
• Date: Wed, 6 Dec 2023 21:30:26 GMT
• Title: Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
• Authors: Dong An, Andrew M. Childs, Lin Lin
• Abstract summary: We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method.
• Score: 5.471398994781521
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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