An improved phase error tolerance in a quantum search algorithm

Abstract

As the matching condition in the Grover search algorithm is transgressed due to inevitable errors in phase inversions, it causes a reduction in the maximum probability of success. With a given degree of maximum success, we have derived a generalized and improved criterion for the tolerated error and the corresponding size of the quantum database under the inevitable gate imperfections. The vanishing inaccurancy of this condition has also been shown. Moreover, a concise formula for evaluating a minimum number of iterations is also presented in this work.