Electron-molecule scattering via R-matrix variational algorithms on a quantum computer
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917485484179456 |
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| author | Picozzi, Dario Tennyson, Jonathan Graves, Vincent Gorfinkiel, Jimena D. |
| author_facet | Picozzi, Dario Tennyson, Jonathan Graves, Vincent Gorfinkiel, Jimena D. |
| contents | Electron-molecule collisions play a central role in both natural processes and modern technological applications, particularly in plasma processing. Conventional computational strategies such as the R-matrix method have been widely adopted yet encounter significant scaling challenges in treating more complex systems. In this work we present a quantum computational approach that utilises the variational quantum eigensolver (VQE) and variations thereof to overcome these limitations. We explore a number of methods, including the use of number projection operators and simultaneous optimisation. We demonstrate the feasibility of our method on a model problem of electron scattering from the hydrogen molecule, with numerical results obtained using a noiseless classical simulator. We recover the full spectrum of the Hamiltonian within a chosen symmetry sector. Moreover, the optimal circuit parameters directly encode the R-matrix boundary amplitudes needed for subsequent scattering computations. To our knowledge, this is the first application of quantum algorithms to electron--molecule scattering, and specifically the first formulation of the R-matrix inner-region problem on a quantum computer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Electron-molecule scattering via R-matrix variational algorithms on a quantum computer Picozzi, Dario Tennyson, Jonathan Graves, Vincent Gorfinkiel, Jimena D. Quantum Physics Electron-molecule collisions play a central role in both natural processes and modern technological applications, particularly in plasma processing. Conventional computational strategies such as the R-matrix method have been widely adopted yet encounter significant scaling challenges in treating more complex systems. In this work we present a quantum computational approach that utilises the variational quantum eigensolver (VQE) and variations thereof to overcome these limitations. We explore a number of methods, including the use of number projection operators and simultaneous optimisation. We demonstrate the feasibility of our method on a model problem of electron scattering from the hydrogen molecule, with numerical results obtained using a noiseless classical simulator. We recover the full spectrum of the Hamiltonian within a chosen symmetry sector. Moreover, the optimal circuit parameters directly encode the R-matrix boundary amplitudes needed for subsequent scattering computations. To our knowledge, this is the first application of quantum algorithms to electron--molecule scattering, and specifically the first formulation of the R-matrix inner-region problem on a quantum computer. |
| title | Electron-molecule scattering via R-matrix variational algorithms on a quantum computer |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.05514 |