Continuous-time quantum walks on a cycle graph (5 pages)

A. Blumen, Oliver Mülken

Dmitry Solenov, Leonid Evgenevich Fedichkin

We present an analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with a nearby quantum point contact. We derive an analytical expression of the probability distribution along the cycle. An upper-bound estimate to the mixing time is shown.

Alexey A. Melnikov, Leonid Evgenevich Fedichkin

We study a continuous-time quantum walk of interacting fermions on a cycle graph. By finding analytical solutions and simulating the dynamics of two fermions we observe a diverse structure of entangled states of indistinguishable fermions. The relation between entanglement of distinguishable qutrits and indistinguishable electrons is observed. Restrictions imposed by the symmetry of a cycle graph are derived. Possible realization of a quantum walk in an array of semiconductor quantum dots is discussed.

S. Salimi

Daniel ben‐Avraham, Eric M. Bollt, Christino Tamon

Dmitry Solenov, Leonid Evgenevich Fedichkin

We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point contact. We derive the analytical expression of the probability distribution along the cycle. Upper bound to mixing time is obtained. It is found to be linear in the graph size.