Accelerated optimization problem search using Bose–Einstein condensation

We investigate a computational device that harnesses the effects of Bose–Einstein condensation to accelerate the speed of finding the solution of optimization problems. Many computationally difficult problems, including NP-complete problems, can be formulated as a ground state search problem. In a Bose–Einstein condensate, below the critical temperature, bosonic particles have a natural tendency to accumulate in the ground state. Furthermore, the speed of attaining this configuration is enhanced as a result of final state stimulation. We propose a physical device that incorporates these basic properties of bosons into the optimization problem, such that an optimized solution is found by a simple cooling of the physical temperature of the device. Using a semiclassical model to calculate the equilibration time for reaching the ground state, we found that this can be sped up by a factor of N , where N is the boson number per site. This allows for the annealing times for reaching a particular error to be systematically decreased by increasing the boson number per site.