Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866915673426362368 |
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| author | An, Dong Childs, Andrew M. Lin, Lin |
| author_facet | An, Dong Childs, Andrew M. Lin, Lin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03916 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters An, Dong Childs, Andrew M. Lin, Lin Quantum Physics Numerical Analysis 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. |
| title | Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters |
| topic | Quantum Physics Numerical Analysis |
| url | https://arxiv.org/abs/2312.03916 |