Quantum Hitting Time on the Complete Graph

Details Quantum Hitting Time on the Complete Graph Quantum Hitting Time on the Complete Graph

2009-12-07

arxiv.org/abs/0912.1217v1

Physics

Quantum Physics

14 pages, 2 figures

Scientific paper

Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important, because it quantifies the running time of the algorithms. Markov chain-based algorithms are probabilistic, therefore the calculation of the success probability is also required in the analysis of the computational complexity. Using Szegedy's definition of quantum hitting time, which is a natural extension of the definition of the classical hitting time, we present analytical expressions for the hitting time and success probability of the quantum walk on the complete graph.

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