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- Title
One-Dimensional Continuous-Time Quantum Walks.
- Authors
ben-Avraham, D.; Bollt, E. M.; Tamon, C.
- Abstract
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 vs. quantum, are strikingly similar in form, although dissimilar in behavior. We also provide comparisons with analyses performed using spectral methods. PACS: 03.67.Lx
- Subjects
LATTICE theory; MARKOV processes; WIENER processes; SIMULATED annealing; STOCHASTIC analysis; EVOLUTION equations; HARMONIC functions; PARTIAL differential equations
- Publication
Quantum Information Processing, 2004, Vol 3, Issue 1-5, p295
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-004-9420-8