Effective Strategy for Non-adjacent Quantum Gates Transformation in Quantum Circuits

This paper proposes an approach to transform a quantum circuit which contains non-adjacent two-qubit gates to an efficient equivalent containing only the adjacent two-qubit gates. We show how to reduce the problem of transforming the quantum circuits into the problem of finding the shortest path in a layered directed acyclic graph. However, the available algorithms to find the shortest path are not efficient enough to solve this problem. Thus, a heuristic algorithm with the runtime of O(mn2) is proposed. Extensive simulations show that the algorithm is efficient and effective enough to find the shortest path, although it does not always guarantee the optimal solution.