A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum Random Walks in One Dimension
Quantum Information Processing
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Decoherence in quantum walks – a review
Mathematical Structures in Computer Science
Continuous-time quantum walks on semi-regular spidernet graphs via quantum probability theory
Quantum Information Processing
On mixing in continuous-time quantum walks on some circulant graphs
Quantum Information & Computation
Mixing and decoherence in continuous-time quantum walks on cycles
Quantum Information & Computation
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Localization of quantum walks can be characterized by the return probability, i.e., theprobability for the walker returning to its original site. In this paper, we consider localiza-tion of continuous-time quantum walks in terms of return probability on a deterministicrecursive tree, which is generated by adding one node and connecting it to each node ofthe existing tree recursively. We obtain an approximate form for the return probabilityusing the complete eigenvalues and eigenstates of Laplace matrix of the structure. It isfound that the return probability depends on the initial node of the excitation. Whenthe walk starts at the central nodes, the return probability converges to a constant valueeven in the limit of infinite system, in contrast to an exponential decay of the returnprobability if the walk starts at the outlying nodes. We also observe a bipartite structurefor the distribution of return probability, and provide theoretical interpretation for allour findings. Our results suggest that quantum walks display significant localization andwell-bedded structure of return probability on heterogeneous trees.