Mixing
and decoherence in quantum walks on cycles
(pp263-276)
Leonid
Fedichkin, Dmitry Solenov, and Christino Tamon
doi:
https://doi.org/10.26421/QIC6.3-3
Abstracts:
We prove analytical results showing that decoherence can be useful for
mixing time in a continuous-time quantum walk on finite cycles. This
complements the numerical observations by Kendon and Tregenna (Physical
Review A 67 (2003),
042315) of a similar phenomenon for discrete-time quantum walks. Our
analytical treatment of continuous-time quantum walks includes a
continuous monitoring of all vertices that induces the decoherence
process. We identify the dynamics of the probability distribution and
observe how mixing times undergo the transition from quantum to
classical behavior as our decoherence parameter grows from zero to
infinity. Our results show that, for small rates of decoherence, the
mixing time improves linearly with decoherence, whereas for large rates
of decoherence, the mixing time deteriorates linearly towards the
classical limit. In the middle region of decoherence rates, our
numerical data confirms the existence of a unique optimal rate for which
the mixing time is minimized.
Key words:
quantum walks, continuous-time, mixing,
decoherence |