Noise effects in the quantum search algorithm from the computational   complexity point of view
  We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm. We show that only for small amounts of noise the quantum search algorithm is still more efficient than any classical algorithm. 
Piotr Gawron, Jerzy Klamka, Ryszard Winiarczyk
quant-ph cs.CC