We propose a combinatorial optimization procedure based on the physical idea of using the quantum tunnel effect to allow the search of global minima of a function of many Boolean variables to escape from poor local minima. More specifically, the function V to be minimized is viewed as the potential energy term in a Schrödinger Hamiltonian H for a quantum spin 1/2 system, the kinetic energy term being the generator of a random walk tailored to the neighborhood structure associated with V The distorted random walk associated with (a suitable approximation of) the ground state eigenfunction of H defines then our approximate optimization strategy. A numerical application to the graph partitioning problem is presented. © 1989.
Apolloni, B., Carvalho, C., & de Falco, D. (1989). Quantum stochastic optimization. Stochastic Processes and Their Applications, 33(2), 233–244. https://doi.org/10.1016/0304-4149(89)90040-9