Exact quantum lower bound for grover's problem

Authors:
Cătălin Dohotaru;Peter Høyer
Affiliations:
Department of Computer Science, University of Calgary, University Drive N.W, Calgary, Alberta, Canada;Department of Computer Science, University of Calgary, University Drive N.W, Calgary, Alberta, Canada
Venue:
Quantum Information & Computation
Year:
2009

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Abstract

One of the most important quantum algorithms ever discovered is Grover's algorithm forsearching an unordered set. We give a new lower bound in the query model which provesthat Grover's algorithm is exactly optimal. Similar to existing methods for proving lowerbounds, we bound the amount of information we can gain from a single oracle query,but we bound this information in terms of angles. This allows our proof to be simple,self-contained, based on only elementary mathematics, capturing our intuition, whileobtaining at the same time an exact bound.