Advancements in Quantum Computing: Solving the Bethe-Salpeter Equation

A recent paper titled "Solving the homogeneous Bethe-Salpeter equation with a quantum annealer" presents significant advancements in quantum computing applications within high-energy physics. The authors, including Filippo Fornetti, Alex Gnech, and Tobias Frederico, successfully solved the homogeneous Bethe-Salpeter equation (hBSE) for the first time using a D-Wave quantum annealer. This equation is crucial for describing bound systems in a relativistic quantum-field theory framework.

The researchers transformed the hBSE into a generalized eigenvalue problem (GEVP) involving two square matrices—one symmetric and one non-symmetric. The challenge lay in developing a formal approach to investigate the non-symmetric GEVP using a quantum annealer, which required recasting it as a quadratic unconstrained binary optimization problem.

The study included a comprehensive numerical analysis of the proposed algorithms, applied to matrices of dimensions up to 64, utilizing both the proprietary simulated-annealing package and the D-Wave Advantage 4.1 system. The results demonstrated a strong correlation with outcomes obtained from standard classical algorithms, highlighting interesting scalability features.

This research not only marks a milestone in quantum computing but also opens avenues for further exploration in high-energy physics, potentially impacting how complex quantum systems are analyzed and understood. The findings are documented in detail in the paper available on arXiv, which can be cited as arXiv:2406.18669.