Continuous-time quantum walk based on cycle under broken-line decoherent noise

Abstract

At present, decoherence continuous-time quantum walks are only based on measurement decoherence, but a new broken-line noise model for continuous-time quantum walks on the cycle is proposed. In this scheme, we first construct the Hamiltonian H according to four cases including no broken links, the link to the left of the node is broken, the link to the right of the node is broken, and both links are broken, and then the probability of a walker is reconstructed. The analysis shows that with the increase of the probability of disconnection, the oscillation of the walk gradually weakens and becomes a peak distribution, and with the continuous increase of the walk time, the probability distribution of each vertex tends to be uniform. In addition, we also analyze the mixing time of this walk model and find that a small amount of broken chain decoherence can help reduce the mixing time, thereby improving the performance of quantum walks.