Efficient Quantum Optimization via Dissipative False Vacuum Decay

Efficient quantum solvers for computationally hard problems are highly desirable for near-term quantum platforms. Here, we propose a cavity-based dissipative quantum solver for a class of NP-hard combinatorial optimization problems encoded in atomic-spin Hamiltonians with a few discrete single-spin-flip transition energies. We show that the cavity-based quantum solver exploits dissipative false-vacuum decay in configuration space to facilitate escape from metastable local minima in rugged energy landscapes. Numerical studies of MaxCut and Maximum Independent Set identify favorable parameter regions for ground-state preparation. Based on the finite-size scalings of the median mixing time and instance-averaged ground-state preparation probability, we estimate time complexities for our solver that are more favorable than those of standard Grover search. These results highlight cavity dissipation as a controllable resource for quantum optimization.