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- Title
Hitting time of quantum walks with perturbation.
- Authors
Chiang, Chen-Fu; Gomez, Guillermo
- Abstract
The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is bounded from above by the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.
- Subjects
QUANTUM theory; PERTURBATION theory; MARKOV processes; RANDOM walks; ALGORITHMS; SQUARE root; MATHEMATICAL bounds
- Publication
Quantum Information Processing, 2013, Vol 12, Issue 1, p217
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-012-0368-9