Reversible circuit rewriting with simulated annealing

This paper presents a rule based approach to optimize the quantum cost of reversible circuits using circuit rewriting rules that handle positive and negative controls. Since incremental optimization cannot guarantee optimality, we consider the application of simulated annealing to find further sub-circuits that could be replaced with smaller ones. Experimental evaluations show that simulated annealing not only can significantly improve the quality of reversible circuits but also is more efficient than a comparable greedy approach. Using the rewriting rules combined with the proposed method quantum cost reductions by up to 80% can be achieved.