Solving graph problems using permutation-invariant quantum machine learning
Fuente:
arXiv
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| Autori principali: | , , , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916746026287104 |
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| author | Mansky, Maximilian Balthasar Rohe, Tobias Stenzel, Gerhard de la Serna, Alejandro Bravo Castillo, Santiago Londoño Sathish, Gautham Nikolaidou, Dimitra Bondarenko, Dmytro Menzel, Linus Linnhoff-Popien, Claudia |
| author_facet | Mansky, Maximilian Balthasar Rohe, Tobias Stenzel, Gerhard de la Serna, Alejandro Bravo Castillo, Santiago Londoño Sathish, Gautham Nikolaidou, Dimitra Bondarenko, Dmytro Menzel, Linus Linnhoff-Popien, Claudia |
| contents | Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond to the specific symmetry of the problem. We investigate this adaption of the quantum circuit to the problem symmetry on graph classification problems. On random graphs, the quantum machine learning ansatz classifies whether a given random graph is connected, bipartite, contains a Hamiltonian path or cycle, respectively. We find that if the quantum circuit reflects the inherent symmetry of the problem, it vastly outperforms the standard, unsymmetrized ansatzes. Even when the symmetry is only approximative, there is still a significant performance gain over non-symmetrized ansatzes. We show how the symmetry can be included in the quantum circuit in a straightforward constructive method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving graph problems using permutation-invariant quantum machine learning Mansky, Maximilian Balthasar Rohe, Tobias Stenzel, Gerhard de la Serna, Alejandro Bravo Castillo, Santiago Londoño Sathish, Gautham Nikolaidou, Dimitra Bondarenko, Dmytro Menzel, Linus Linnhoff-Popien, Claudia Quantum Physics Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond to the specific symmetry of the problem. We investigate this adaption of the quantum circuit to the problem symmetry on graph classification problems. On random graphs, the quantum machine learning ansatz classifies whether a given random graph is connected, bipartite, contains a Hamiltonian path or cycle, respectively. We find that if the quantum circuit reflects the inherent symmetry of the problem, it vastly outperforms the standard, unsymmetrized ansatzes. Even when the symmetry is only approximative, there is still a significant performance gain over non-symmetrized ansatzes. We show how the symmetry can be included in the quantum circuit in a straightforward constructive method. |
| title | Solving graph problems using permutation-invariant quantum machine learning |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.12764 |