Effective Hash-Based Algorithm for Reversible Logic Circuits Synthesis with Minimum Cost

We present an effective algorithm which can construct optimal 3-qubit reversible logic circuits for any given reversible logic gates and costs by constructing a minimal perfect hash function. We also present an algorithm which can automatically construct quantum gate library. In the experiments on 3-qubit synthesis, our algorithm synthesizes all optimal reversible circuits with extremely fast speed--the average speed which synthesizes circuits with minimum cost is 365 times faster than that of best result.