Mixing and decoherence in continuous-time quantum walks on cycles

  • Authors:

  • Leonid Fedichkin;Dmitry Solenov;Christino Tamon

  • Affiliations:

  • Center for Quantum Device Technology, Department of Physics, and Department of Electrical and Computer Engineering, Clarkson University, Potsdam NY;Center for Quantum Device Technology and Department of Physics, Clarkson University, Potsdam NY;Department of Mathematics and Computer Science and Center for Quantum Device Technology, Clarkson University, Potsdam NY

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2006

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Abstract

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 analygicM treatment of continuous-time quantum walks includes a continuous monitoring of all vertices that induces the decoherence process. We identify the dymamics 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 confirnm the existence of a unique optimal rate for which the mixing time is minimized.