Effects of systematic phase errors on optimized quantum random-walk search algorithm

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

This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover’s algorithm.

Hristo Tonchev, Petar Danev

Yun Li, Lei Ma, Jie Zhou

We study how imperfect quantum gates affect the quantum random-walk search algorithm. We find that systematic errors in phase inversions result in the reduction of the maximum probability of the marked state and lower the algorithm efficiency with an increasing degree of inaccuracy. The size of the database should be limited due to the inevitable errors. Finally, we compare the phase noise caused by such errors in the random-walk search algorithm with that in the Grover search algorithm.

Xin Li, Cheng Cheng, Chuntian +4 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.

Uğur Küçük, A. C. Cem Say