The effect of decoherence on mixing time in continuous-time quantum walks on one-dimension regular networks

摘要

In this paper, we study decoherence in continuous-time quantum walks (CTQWs)on one-dimension regular networks. For this purpose, we assume that every nodeis represented by a quantum dot continuously monitored by an individual pointcontact(Gurvitz's model). This measuring process induces decoherence. We focuson small rates of decoherence and then obtain the mixing time bound of theCTQWs on one-dimension regular network which its distance parameter is $l\geq2$. Our results show that the mixing time is inversely proportional to rate ofdecoherence which is in agreement with the mentioned results for cycles in\cite{FST,VKR}. Also, the same result is provided in \cite{SSRR} for long-rangeinteracting cycles. Moreover, we find that this quantity is independent ofdistance parameter $l(l\geq 2)$ and that the small values of decoherence makeshort the mixing time on these networks.