A Quantum Algorithm for Finding the Minimum
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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.
[1] Gilles Brassard,et al. Strengths and Weaknesses of Quantum Computing , 1997, SIAM J. Comput..
[2] Lov K. Grover. A fast quantum mechanical algorithm for database search , 1996, STOC '96.
[3] Gilles Brassard,et al. Tight bounds on quantum searching , 1996, quant-ph/9605034.