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The continuous-time quantum walk on some graphs based on the view of quantum probability.
- Source :
-
International Journal of Quantum Information . Sep2022, Vol. 20 Issue 6, p1-13. 13p. - Publication Year :
- 2022
-
Abstract
- In this paper, continuous-time quantum walk is discussed based on the view of quantum probability, i.e. the quantum decomposition of the adjacency matrix A of graph. Regard adjacency matrix A as Hamiltonian which is a real symmetric matrix with elements 0 or 1, so we regard  e − i t A  as an unbiased evolution operator, which is related to the calculation of probability amplitude. Combining the quantum decomposition and spectral distribution  μ  of adjacency matrix A, we calculate the probability amplitude reaching each stratum in continuous-time quantum walk on complete bipartite graphs, finite two-dimensional lattices, binary tree, N -ary tree and N -fold star power G ⋆ N . Of course, this method is also suitable for studying some other graphs, such as growing graphs, hypercube graphs and so on, in addition, the applicability of this method is also explained. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02197499
- Volume :
- 20
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- International Journal of Quantum Information
- Publication Type :
- Academic Journal
- Accession number :
- 158678630
- Full Text :
- https://doi.org/10.1142/S0219749922500150