Constant-Time Solution to Simon's Decision Problem with the Known Subgroup Range in Quantum Computer

C.-Y. Chen and C.-C. Hsueh (Taiwan)


Quantum computing, Simon’s algorithm


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.

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