Quantum annealing

Quantum annealing Quantum annealing (also known as alloy, crystallization or tempering) is analogous to simulated annealing but in substitution of thermal activation by quantum tunneling. The class of algorithmic methods for quantum annealing (dubbed: 'QA'), sometimes referred by the italian school as Quantum Stochastic Optimization ('QSO'), is a promising metaheuristic tool for solving local search problems in multivariable optimization contexts. These problems usually consist in finding the maximum or minimum for a cost function that comprises several independent variables and a large number of instances. The evaluation of cost in this context must necessarily be computed in probabilistic terms, as given the large amplitude of the space of configurations (frequently hamiltonian matrices with the huge dimension of 2 N rows), the most common case is that an explicit, exhaustive evaluation of them all can not be performed because they are excessively numerous to be calculated in a reasonably practical time interval. Let's think that, for a glass network with only five nodes, a 2 5 *2 5 ~= 1000 elements matrix would need to be operated upon; with only ten nodes, this is boosted to over one million elements, and with sixteen nodes, to a whooping 4,300,000,000 (we dub this " the curse of dimensionality " or " Hughes effect " , due to Bellman). A single configuration is thus defined as a 'tuple' (or 'array') of values over the whole set of independent variables. The value of the cost function depends on the configurations, being the solution to the problem set as the definite optimal configuration which minimizes, or maximizes, the cost function with some arbitrarily chosen confidence level or probability. In some way, all methods for annealing, alloy, tempering or crystallization are a metaphor of nature that tries to imitate the way in which the molecules of a metal do order when magnetization occurs, or of a crystal during the phase transition that happens for instance, when water freezes or silicon dioxide crystallizes after having been previously heated up enough to break its chemical bonds. If the cooling is slow enough ('tempering'), then the crystal generated this way will usually exhibit less imperfections (this is to say, it will be found in a lower energy metastate) than if it is frozen too fast (higher energy metastate). This physical model of nature is based upon the trend to minimize its free energy (in a Helmholtz sense) of any ergodic …