Raqueline A. M. Santos, Renato Portugal, Marcelo D. Fragoso
Quantum walks have been used for developing quantum algorithms that outperform their classical analogues. In the context of spatial search algorithms, quantum hitting time plays an important role as the algorithm's stopping time. In this work, we analyze a decoherence model on Szegedy's quantum walk, based on percolation graphs. By performing averages over all possible evolution operators affected by the decoherence, we show that it is possible to define a decoherent quantum hitting time and to prove that the quadratic speedup for the quantum hitting time is still valid when the percolation probability is small.
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http://arxiv.org/abs/1204.6238
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