Optimal Quantum Circuits of Three Qubits

This paper shows how to find the optimal quantum circuits for all 3-qubit functions with an exhaustive search. A circuit for a given function is said to be optimal, if no realization with fewer gates exists. It is important to have the optimal results for all three-input functions, since they can serve as benchmarks when evaluation heuristic optimization algorithms. The optimal results generated, are compared with optimized quantum circuits obtained from post synthesis algorithms. It is observed that the published templates do not lead to optimal results. Experimental results show, that optimal circuits can seldom be obtained with template matching. On average the optimal size of a 3-qubit circuit is 10.0, where as template matching only achieves an average of 11.9 gates. It is shown that this is due to the fact that not all templates have been discovered. The paper concludes with some directions for further research.