One-dimensional continuous-time quantum walks

Details One-dimensional continuous-time quantum walks One-dimensional continuous-time quantum walks

2004-09-20

arxiv.org/abs/cond-mat/0409514v1

Quantum Information Processing 3, 295-308 (2004)

Physics

Condensed Matter

Other Condensed Matter

10 pages, 4 figures, to appear in Quantum Information Processing

Scientific paper

We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of our expository article is on analyzing these processes using the Laplace transform on the stochastic recurrences. The resulting time evolution equations, classical versus quantum, are strikingly similar in form, although dissimilar in behavior. We also provide comparisons with analyses performed using spectral methods.

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