Zero transfer in continuous-time quantum walks
- 35 Downloads
In this paper, we show how using complex-valued edge weights in a graph can completely suppress the flow of probability amplitude in a continuous-time quantum walk to specific vertices of the graph when the edge weights, graph topology, and initial state of the quantum walk satisfy certain conditions. The conditions presented in this paper are derived from the so-called chiral quantum walk, a variant of the continuous-time quantum walk which incorporates directional bias with respect to site transfer probabilities between vertices of a graph by using complex edge weights. We examine the necessity to break the time-reversal symmetry in order to achieve zero transfer in continuous-time quantum walks. We also consider the effect of decoherence on zero transfer and suggest that this phenomenon may be used to detect and quantify decoherence in the system.
KeywordsChiral quantum walk Zero transfer Quantum stochastic walk Lindblad equation
We would like to thank Aeysha Khalique for proof reading the manuscript and providing constructive suggestions.
- 2.Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Foundations of Computer Science, 1994 Proceedings, 35th Annual Symposium on (IEEE), pp. 124–134 (1994)Google Scholar
- 20.Qiang, X., Zhou, X., Wang, J., Wilkes, C.M., Loke, T., O’Gara, S., Kling, L., Marshall, G.D., Santagati, R., Ralph, T.C., Wang, J.B., O’Brien, J.L., Thompson, M.G., Matthews, J.C.F.: Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nat. Photonics (to appear, 2018)Google Scholar
- 21.Childs, A.M., Cleve, R., Deotto, E., Farhi, E., Gutmann, S., Spielman, D.A.: Exponential algorithmic speedup by a quantum walk. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing (ACM), pp. 59–68 (2003)Google Scholar