Experiments on Quantum Annealing

Abstract

The standard deterministic, gate-based computation paradigms underlying modern digital computing are not those that nature uses to perform complex tasks such as finding the lowest energy states of spin glasses or proteins. Instead, for such complex problems, natural processes achieve their optima by trial and error, where the extent to which ‘errors’ are accepted is determined by the system temperature. Optima then follow by slow cooling from a hightemperature, annealed state. Nearly three decades ago, Kirkpatrick, Gelatt and Vecchi [1] suggested that for certain complex computational problems, including for example that of the travelling salesman, it may be more productive to simulate natural annealing and cooling on a computer, using standard Monte Carlo routines, rather than attempting to use classical mathematical algorithms to find solutions. The appeal of simulated annealing is not only that it can be applied to essentially any new optimization problem, but also that it provides a language, namely that of the thermodynamics of complex statistical mechanical systems, for describing why and how optima can be reached. Motivated by this early work, we asked [2] the question of whether quantum rather than thermal .uctuations could be used to relax a system of many interacting degrees of freedom. The reason why this seemed like a good question to ask is illustrated in Fig. 1 – quantum tunnelling makes transitions to regions of phase space possible that might be very dificult to access via classical, thermal barrier hopping.