Quantum walk approach to search on fractal structures

Details Quantum walk approach to search on fractal structures Quantum walk approach to search on fractal structures

2010-02-05

arxiv.org/abs/1002.1274v2

Phys. Rev. A 82, 012305 (2010)

Physics

Quantum Physics

15 pages, 14 figures

Scientific paper

10.1103/PhysRevA.82.012305

We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the topological structure of the database plays a crucial role by analyzing, both analytically and numerically, the transition from the ground to the first excited state of the Hamiltonian associated with different (fractal) structures. Additionally, we use the probability of successfully finding a specific target as another indicator of the importance of the topological structure.

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