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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.18669 |
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| _version_ | 1866929479059767296 |
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| author | Fornetti, Filippo Gnech, Alex Frederico, Tobias Pederiva, Francesco Rinaldi, Matteo Roggero, Alessandro Salme', Giovanni Scopetta, Sergio Viviani, Michele |
| author_facet | Fornetti, Filippo Gnech, Alex Frederico, Tobias Pederiva, Francesco Rinaldi, Matteo Roggero, Alessandro Salme', Giovanni Scopetta, Sergio Viviani, Michele |
| contents | The homogeneous Bethe-Salpeter equation (hBSE), describing a bound system in a genuinely relativistic quantum-field theory framework, was solved for the first time by using a D-Wave quantum annealer. After applying standard techniques of discretization, the hBSE, in ladder approximation, can be formally transformed in a generalized eigenvalue problem (GEVP), with two square matrices: one symmetric and the other non symmetric. The latter matrix poses the challenge of obtaining a suitable formal approach for investigating the non symmetric GEVP by means of a quantum annealer, i.e to recast it as a quadratic unconstrained binary optimization problem. A broad numerical analysis of the proposed algorithms, applied to matrices of dimension up to 64, was carried out by using both the proprietary simulated-anneaing package and the D-Wave Advantage 4.1 system. The numerical results very nicely compare with those obtained with standard classical algorithms, and also show interesting scalability features. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving the homogeneous Bethe-Salpeter equation with a quantum annealer Fornetti, Filippo Gnech, Alex Frederico, Tobias Pederiva, Francesco Rinaldi, Matteo Roggero, Alessandro Salme', Giovanni Scopetta, Sergio Viviani, Michele High Energy Physics - Phenomenology Quantum Physics The homogeneous Bethe-Salpeter equation (hBSE), describing a bound system in a genuinely relativistic quantum-field theory framework, was solved for the first time by using a D-Wave quantum annealer. After applying standard techniques of discretization, the hBSE, in ladder approximation, can be formally transformed in a generalized eigenvalue problem (GEVP), with two square matrices: one symmetric and the other non symmetric. The latter matrix poses the challenge of obtaining a suitable formal approach for investigating the non symmetric GEVP by means of a quantum annealer, i.e to recast it as a quadratic unconstrained binary optimization problem. A broad numerical analysis of the proposed algorithms, applied to matrices of dimension up to 64, was carried out by using both the proprietary simulated-anneaing package and the D-Wave Advantage 4.1 system. The numerical results very nicely compare with those obtained with standard classical algorithms, and also show interesting scalability features. |
| title | Solving the homogeneous Bethe-Salpeter equation with a quantum annealer |
| topic | High Energy Physics - Phenomenology Quantum Physics |
| url | https://arxiv.org/abs/2406.18669 |