Quantum kernel methods for solving regression problems and differential equations
dc.contributor.author | Paine, AE | |
dc.contributor.author | Elfving, VE | |
dc.contributor.author | Kyriienko, O | |
dc.date.accessioned | 2023-04-24T13:32:27Z | |
dc.date.issued | 2023-03-31 | |
dc.date.updated | 2023-04-24T10:59:38Z | |
dc.description.abstract | We propose several approaches for solving regression problems and differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are represented using automatic differentiation of quantum circuits. While previously quantum kernel methods primarily targeted classification tasks, here we consider their applicability to regression tasks, based on available data and differential constraints. We use two strategies to approach these problems. First, we devise a mixed model regression with a trial solution represented by kernel-based functions, which is trained to minimize a loss for specific differential constraints or datasets. Second, we use support vector regression that accounts for the structure of differential equations. The developed methods are capable of solving both linear and nonlinear systems. Contrary to prevailing hybrid variational approaches for parametrized quantum circuits, we perform training of the weights of the model classically. Under certain conditions this corresponds to a convex optimization problem, which can be solved with provable convergence to global optimum of the model. The proposed approaches also favor hardware implementations, as optimization only uses evaluated Gram matrices, but require a quadratic number of function evaluations. We highlight trade-offs when comparing our methods to those based on variational quantum circuits such as the recently proposed differentiable quantum circuits approach. The proposed methods offer potential quantum enhancement through the rich kernel representations using the power of quantum feature maps, and start the quest towards provably trainable quantum DE solvers. | en_GB |
dc.format.extent | 032428- | |
dc.identifier.citation | Vol. 107(3), article 032428 | en_GB |
dc.identifier.doi | https://doi.org/10.1103/physreva.107.032428 | |
dc.identifier.uri | http://hdl.handle.net/10871/133000 | |
dc.identifier | ORCID: 0000-0002-6259-6570 (Kyriienko, Oleksandr) | |
dc.language.iso | en | en_GB |
dc.publisher | American Physical Society (APS) | en_GB |
dc.rights | © 2023. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. | en_GB |
dc.title | Quantum kernel methods for solving regression problems and differential equations | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2023-04-24T13:32:27Z | |
dc.identifier.issn | 2469-9926 | |
exeter.article-number | 032428 | |
dc.description | This is the final version. Available on open access from the American Physical Society via the DPO in this record | en_GB |
dc.identifier.eissn | 2469-9934 | |
dc.identifier.journal | Physical Review A | en_GB |
dc.relation.ispartof | Physical Review A, 107(3) | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_GB |
dcterms.dateAccepted | 2023-03-07 | |
rioxxterms.version | VoR | en_GB |
rioxxterms.licenseref.startdate | 2023-03-31 | |
rioxxterms.type | Journal Article/Review | en_GB |
refterms.dateFCD | 2023-04-24T13:29:17Z | |
refterms.versionFCD | VoR | |
refterms.dateFOA | 2023-04-24T13:32:30Z | |
refterms.panel | B | en_GB |
refterms.dateFirstOnline | 2023-03-31 |
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