Bounds for mixing time of quantum walks on finite graphs

Vladislav Kargin
2010 Journal of Physics A: Mathematical and Theoretical  
Several inequalities are proved for the mixing time of discrete-time quantum walks on finite graphs. The mixing time is defined differently than in Aharonov, Ambainis, Kempe and Vazirani (2001) and it is found that for particular examples of walks on a cycle, a hypercube and a complete graph, quantum walks provide no speed-up in mixing over the classical counterparts. In addition, non-unitary quantum walks (i.e., walks with decoherence) are considered and a criterion for their convergence to
more » ... r convergence to the unique stationary distribution is derived.
doi:10.1088/1751-8113/43/33/335302 fatcat:rl5upwmdnjccpfmxlejpein2vu