2003/10/31 by A. Romanelli, A. C. Sicardi Schifino, A. C. Sicardi-Schifino +4 · 2 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.1016/j.physa.2004.02.061
published as Physica A Volume/Issue338/3-4 pp. 395-405 (2004). · few typos corrected, 13 pages, 2 figures, to appear in Physica A
openalex publication_date 2004/03/18 · arxiv created 2004/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.