A Quantum Algorithm for Finding the Minimum

Let T [0..N −1] be an unsorted table of N items, each holding a value from an ordered set. For simplicity, assume that all values are distinct. The minimum searching problem is to find the index y such that T [y] is minimum. This clearly requires a linear number of probes on a classical probabilistic Turing machine. Here, we give a simple quantum algorithm which solves the problem using O( √ N) probes. The main subroutine is the quantum exponential searching algorithm of [2], which itself is a generalization of Grover’s recent quantum searching algorithm [3]. Due to a general lower bound of [1], this is within a constant factor of the optimum.