Physics – Quantum Physics
Scientific paper
2003-10-29
Physica A Volume/Issue338/3-4 pp. 395-405 (2004).
Physics
Quantum Physics
few typos corrected, 13 pages, 2 figures, to appear in Physica A
Scientific paper
10.1016/j.physa.2004.02.061
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.
Abal Gonzalo
Auyuanet Adriana
Donangelo Raul
Romanelli Alejandro
Sicardi-Schifino A. C.
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