Document Type
Article
Publication Date
2024
DOI
10.1103/PhysRevD.110.056012
Publication Title
Physical Review D
Volume
110
Issue
5
Pages
056012 (1-20)
Abstract
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 nonsymmetric. The latter matrix poses the challenge of obtaining a suitable formal approach for investigating the nonsymmetric 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-annealing 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.
Rights
© 2024 The Authors.
Published under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Original Publication Citation
Fornetti, F., Gnech, A., Frederico, T., Pederiva, F., Rinaldi, M., Roggero, A., Salmè, G., Scopetta, S., & Viviani, M. (2024). Solving the homogeneous Bethe-Salpeter equation with a quantum annealer. Physical Review D, 110(5), 1-20, Article 056012. https://doi.org/10.1103/PhysRevD.110.056012
ORCID
0000-0002-2077-3866 (Gnech)
Repository Citation
Fornetti, Filippo; Gnech, Alex; Frederico, Tobias; Pederiva, Francesco; Rinaldi, Matteo; Roggero, Alessandro; Salmè, Giovanni; Scopetta, Sergio; and Viviani, Michele, "Solving the Homogeneous Bethe-Salpeter Equation with a Quantum Annealer" (2024). Physics Faculty Publications. 878.
https://digitalcommons.odu.edu/physics_fac_pubs/878