White Noise in Quantum Random Walk Search Algorithm

张宇超, 鲍皖苏, 汪翔 +1 more

Лей Ма, Du Jiang-Feng, Yun Li +3 more

The quantum random walk is a possible approach to construct new quantum search algorithms. It has been shown by Shenvi et al. [Phys. Rev. A 67 (2003) 52307 that a kind of algorithm can perform an oracle search on a database of N items with O ( N 1/2 ) calling to the oracle, yielding a speedup similar to other quantum search algorithms. We study the effect of white or Gaussian noise on this algorithm. The algorithm loses efficiency when noise is added. We also show that noise on the target state plays a more important role than that on other states. Finally we compare the effects of similar types of noise in the quantum random walk search algorithm and Grover's search algorithm.

Caishi Wang, Ce Wang, Suling Ren +1 more

Yuchao Zhang, Wan‐Su Bao, Xiang Wang +1 more

This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.

V. P. Belavkin, Jaeseong Heo, Un Cig Ji

Hristo Tonchev, Petar Danev