  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.
