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Quantum random walk on the line as a Markovian process

Author

Listed:
  • Romanelli, A.
  • Sicardi Schifino, A.C.
  • Siri, R.
  • Abal, G.
  • Auyuanet, A.
  • Donangelo, R.

Abstract

We analyze in detail the discrete-time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker's position with time is a direct consequence of the coherence of the quantum evolution. If the evolution is decoherent, as in the classical case, the variance is shown to increase linearly with time, as expected. Furthermore, we show that this system has an evolution operator analogous to that of a resonant quantum kicked rotor. As this rotator may be described through a quantum computational algorithm, one may employ this algorithm to describe the time evolution of the quantum walker.

Suggested Citation

  • Romanelli, A. & Sicardi Schifino, A.C. & Siri, R. & Abal, G. & Auyuanet, A. & Donangelo, R., 2004. "Quantum random walk on the line as a Markovian process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 395-405.
    • Handle: RePEc:eee:phsmap:v:338:y:2004:i:3:p:395-405
    DOI: 10.1016/j.physa.2004.02.061
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    Cited by:

    1. Kang, Yuanbao, 2016. "Quantum decomposition of random walk on Cayley graph of finite group," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 146-156.

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