Constant-time solution to Simon's decision problem with the known subgroup range in quantum computer

Authors:
Chien-Yuan Chen;Chih-Cheng Hsueh
Affiliations:
National University of Kaohsiung, Kaohsiung, Taiwan;I-Shou University, Kaohsiung County, Taiwan, R.O.C.
Venue:
CI '07 Proceedings of the Third IASTED International Conference on Computational Intelligence
Year:
2007

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Abstract

Simon's algorithm can determine whether the function f is bijective or periodic by using the polynomial-function evaluations. Simon's algorithm is more efficient than classical algorithms which require exponential function evaluations. In this paper, we assume that the range of the periodic function is a known subgroup. We further find an integer b orthogonal to the range. According to b, we can construct a quantum algorithm to determine whether f is bijective or periodic in only one function evaluation.