Variational quantum algorithms for nonlinear problems
We show that nonlinear problems including nonlinear partial di↵erential equations can be e- ciently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities eciently and by introducing tensor networks as a programming...
| Hlavní autoři: | , , , , |
|---|---|
| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
American Physical Society
2020
|
| _version_ | 1826303261384114176 |
|---|---|
| author | Lubasch, M Joo, J Moinier, P Kiffner, M Jaksch, D |
| author_facet | Lubasch, M Joo, J Moinier, P Kiffner, M Jaksch, D |
| author_sort | Lubasch, M |
| collection | OXFORD |
| description | We show that nonlinear problems including nonlinear partial di↵erential equations can be e- ciently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities eciently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr¨odinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more ecient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device. |
| first_indexed | 2024-03-07T05:59:58Z |
| format | Journal article |
| id | oxford-uuid:ebd47ad9-8cdd-44cd-926f-258c3da098e7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:59:58Z |
| publishDate | 2020 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:ebd47ad9-8cdd-44cd-926f-258c3da098e72022-03-27T11:12:58ZVariational quantum algorithms for nonlinear problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ebd47ad9-8cdd-44cd-926f-258c3da098e7EnglishSymplectic Elements at OxfordAmerican Physical Society2020Lubasch, MJoo, JMoinier, PKiffner, MJaksch, DWe show that nonlinear problems including nonlinear partial di↵erential equations can be e- ciently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities eciently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr¨odinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more ecient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device. |
| spellingShingle | Lubasch, M Joo, J Moinier, P Kiffner, M Jaksch, D Variational quantum algorithms for nonlinear problems |
| title | Variational quantum algorithms for nonlinear problems |
| title_full | Variational quantum algorithms for nonlinear problems |
| title_fullStr | Variational quantum algorithms for nonlinear problems |
| title_full_unstemmed | Variational quantum algorithms for nonlinear problems |
| title_short | Variational quantum algorithms for nonlinear problems |
| title_sort | variational quantum algorithms for nonlinear problems |
| work_keys_str_mv | AT lubaschm variationalquantumalgorithmsfornonlinearproblems AT jooj variationalquantumalgorithmsfornonlinearproblems AT moinierp variationalquantumalgorithmsfornonlinearproblems AT kiffnerm variationalquantumalgorithmsfornonlinearproblems AT jakschd variationalquantumalgorithmsfornonlinearproblems |