Quantum Algorithms for Highly Structured Search Problems

Authors:
Markus Hunziker;David A. Meyer
Affiliations:
Project in Geometry and Physics, Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112. Present address: Department of Mathematics, University of Georgia, ...;Project in Geometry and Physics, Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112. E-mail: dmeyer@math.ucsd.edu
Venue:
Quantum Information Processing
Year:
2002

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Abstract

We consider the problem of identifying a base k string given an oracle which returns information about the number of correct components in a query, specifically, the Hamming distance between the query and the solution, modulo r = max{2, 6 − k}. Classically this problem requires Ω(n logrk) queries. For k ∈ {2, 3, 4}, we construct quantum algorithms requiring only a single quantum query. For k 4, we show that O(√k) quantum queries suffice. In both cases the quantum algorithms are optimal.PACS: 03.67.Lx