Optimizing the number of gates in quantum search
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Published:2017-03
Issue:3&4
Volume:17
Page:251-261
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ISSN:1533-7146
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Container-title:Quantum Information and Computation
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language:
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Short-container-title:QIC
Author:
Arunachalam Srinivasan,de Wolf Ronald
Abstract
In its usual form, Grover’s quantum search algorithm uses O( √ N) queries and O( √ N log N) other elementary gates to find a solution in an N-bit database. Grover in 2002 showed how to reduce the number of other gates to O( √ N log log N) for the special case where the database has a unique solution, without significantly increasing the number of queries. We show how to reduce this further to O( √ N log(r) N) gates for every constant r, and sufficiently large N. This means that, on average, the circuits between two queries barely touch more than a constant number of the log N qubits on which the algorithm acts. For a very large N that is a power of 2, we can choose r such that the algorithm uses essentially the minimal number π 4 √ N of queries, and only O( √ N log(log? N)) other gates.
Subject
Computational Theory and Mathematics,General Physics and Astronomy,Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics,Theoretical Computer Science
Cited by
1 articles.
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