Superconducting Neural Network for Solving a Combinatorial Optimization Problem

We propose a neural network using coupled-SQUIDs to solve the N-Queens problem, a combinatorial optimization problem. The N-Queen problem consists of placing N queens on an N × N chess board such that none of the queens are able to capture any other using standard chess moves for a queen. We run a numerical simulation to show that a network consisting of a combination of coupled-SQUIDs can arrive at the solution. However, conditions of the network may be trapped in incorrect answers due to the existence of local minima on the energy function of the network. The Josephson voltage oscillation effect is effective for escaping from such conditions due to the existence of local minima. We investigate network dynamics and discuss the performance of the network on the basis of the parameters of the Nb integration circuit.