Quantum walks for crossed cubes

This paper proposes a quantum switching on crossed cube, the diameter of the crossed cube is almost half of that of the hypercube, to execute quantum walks. Quantum walks can be implemented in the hypercube and general graphs. Hypercube is a regular graph. According to quantum walk algorithm, the system can preserve unitary property of quantum walks. In the regular graph, to develop quantum walks algorithm is focused on quantum search algorithm. The proposed circuit is to use quantum state, transferring from source node to destination for find the searching object. The small diameter is the best criterion to simulate the behavior of the proposed mechanism. This work selects crossed cube as the research topics with the following two major clauses. One is the small diameter and the other is the exchanged crossed state. The crossed cube has the half diameter of the hypercube. This cube owns the exchanged crossed state that can be used to present the behavior of the entangled particles. Quantum switching is reversible circuit and parallel computation circuit. By using parallel computation circuit, the system can achieve the better performance in time complexity and space complexity. Based on quantum switching, the system can trace the behavior of quantum walks from input sequence to output sequence, and obtains the benefit in time complexity and space complexity for quantum search algorithm.