A Quantum Algorithm for Finding the Minimum

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