Improved Local Field Response Method Working as Quasi-Quantum Annealing

The local-field response (LFR) method is a way of searching for the ground state of an Ising spin Hamiltonian. Spins evolve by responding to an effective field consisting of gradually decreasing external transverse fields and spin-spin interactions. The spins are treated as classical variables, but quantum effects are taken into account in the response of the spins. The conventional LFR method takes a quantum effect into account through an a priori determined response function. This report not only uses the response function but also considers quantum effects more directly. (1) The effect of band anticrossing is considered. (2) The interaction term and local term in the effective field are appropriately balanced by renormalizing the local term. (3) The a priori determined response function is modified on the basis of a self-field correction. In addition to these quantum-mechanical improvements, (4) the transverse field is modulated with a saw shape to increase opportunities of finding the global minimum, and all spins are inverted several times in the middle of the process in order to expand the search space. As a result, the false probability, the inaccuracy of the solution, and the average number of steps before reaching the final solution decrease to about one-tenth of the corresponding values for the case without improvements.