One-Dimensional Continuous-Time Quantum Walks

Authors:
D. Ben-Avraham;E. M. Bollt;C. Tamon
Affiliations:
Department of Physics, Clarkson University, USA;Department of Mathematics and Computer Science, and Department of Physics, Clarkson University, USA;Department of Mathematics and Computer Science, and Center for Quantum Device Technology, Clarkson University, USA/ Department of Physics, Clarkson University, USA
Venue:
Quantum Information Processing
Year:
2004

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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.