Investigation of continuous-time quantum walks via spectral analysis and Laplace transform

2007/04/19 by M. A. Jafarizadeh, Jafarizadeh, M. A., R. Sufiani +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #quant-ph

paper · pdf · doi:10.48550/arxiv.0704.2602

28 pages

arxiv created 2007/04/19 · openalex publication_date 2007/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Continuous-time quantum walk (CTQW) on a given graph is investigated by using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with the graph. It is shown that, the probability amplitude of observing the CTQW at a given site at time t is related to the inverse Laplace transformation of the Stieltjes function, namely, one can calculate the probability amplitudes only by taking the inverse laplace transform of the function iG_μ(is), where G_μ(x) is the Stieltjes function of the graph. The preference of this procedure is that, there is no any need to know the spectrum of the graph

Citations

• Quantum Computation and Decision Trees

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