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Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm
, Article European Physical Journal B ; Volume 59, Issue 2 , 2007 , Pages 199-216 ; 14346028 (ISSN) ; Sufiani, R ; Salimi, S ; Jafarizadeh, S ; Sharif University of Technology
2007
Abstract
In papers [Jafarizadehn and Salimi, Ann. Phys. 322, 1005 (2007) and J. Phys. A: Math. Gen. 39, 13295 (2006)], the amplitudes of continuous-time quantum walk (CTQW) on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated with their adjacency matrix. Here in this paper, it is shown that the CTQW on any arbitrary graph can be investigated by spectral analysis method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition (GQD) have been introduced, where...