Optimization by a quantum reinforcement algorithm
This is an incremental approach for researchers in quantum computing, potentially aiding in solving computationally hard optimization problems.
The paper tackled the problem of solving classical optimization problems by introducing a quantum reinforcement algorithm that localizes a quantum particle's wave function on optimal configurations, with numerical simulations showing it increases the minimal energy gap in quantum annealing for small problem sizes.
A reinforcement algorithm solves a classical optimization problem by introducing a feedback to the system which slowly changes the energy landscape and converges the algorithm to an optimal solution in the configuration space. Here, we use this strategy to concentrate (localize) preferentially the wave function of a quantum particle, which explores the configuration space of the problem, on an optimal configuration. We examine the method by solving numerically the equations governing the evolution of the system, which are similar to the nonlinear Schrödinger equations, for small problem sizes. In particular, we observe that reinforcement increases the minimal energy gap of the system in a quantum annealing algorithm. Our numerical simulations and the latter observation show that such kind of quantum feedbacks might be helpful in solving a computationally hard optimization problem by a quantum reinforcement algorithm.