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Nature Physics

Needling the haystack

Jacob Dunningham

Published Oct 1, 2010• 0 citations
Publisher
DOI
10.1038/nphys1795

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If we want to break someone else's PIN (personal identification number) of, say, an ATM (automated teller machine), how many trials would be necessary when we want to be efficient? This is a sort of what we calla-needle-in-a-hay-stackproblem. In 1987, in their wonderful paper, Hinton & Nowlan proposed a genetic algorithm with a needle being a unique configuration of 20-bit binary string while all other configurations being a haystack. What they proposed was to exploit alifetimelearningof individuals in their genetic algorithm, calling it the Baldwin effectinacomputer. Since then there has been a fair amount of exploration of this effect, claiming, "this is a-needle-in-a-hay-stack problem, and we've found a more efficient algorithm than a random search." Some of them, however, were found to be the results of an effect oflike-to-hear-what-we-would-like-to-hear. In this talk, we will try a bird's eye view on a few examples we have had so far, and how they were explored, including the approach by means of quantum computation which claims, "The steps to find a needle areO(radicN) while those of exhaustive search by a traditional computer are O(N) whereNis the number of search points."
The search for ``a quantum needle in a quantum haystack'' is a metaphor for the problem of finding out which one of a permissible set of unitary mappings---the oracles---is implemented by a given black box. Grover's algorithm solves this problem with quadratic speedup as compared with the analogous search for ``a classical needle in a classical haystack.'' Since the outcome of Grover's algorithm is probabilistic---it gives the correct answer with high probability, not with certainty---the answer requires verification. For this purpose we introduce specific test states, one for each oracle. These test states can also be used to realize ``a classical search for the quantum needle'' which is deterministic---it always gives a definite answer after a finite number of steps---and 3.41 times as fast as the purely classical search. Since the test-state search and Grover's algorithm look for the same quantum needle, the average number of oracle queries of the test-state search is the classical benchmark for Grover's algorithm.