Intricacies of quantum computational paths

Intricacies of quantum computational paths Graph search represents a cornerstone in computer science and is employed when the best algorithmic solution to a problem consists in performing an analysis of a search space representing computational possibilities. Typically, in such problems it is crucial to determine the sequence of transitions performed that led to certain states. In this work we discuss how to adapt generic quantum search procedures, namely quantum random walks and Grover’s algorithm, in order to obtain computational paths. We then compare these approaches in the context of tree graphs. In addition we demonstrate that in a best-case scenario both approaches differ, performance-wise, by a constant factor speedup of two, whilst still providing a quadratic speedup relatively to their classical equivalents. We discuss the different scenarios that are better suited for each approach. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Intricacies of quantum computational paths

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Publisher
Springer US
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-012-0475-7
Publisher site
See Article on Publisher Site

Abstract

Graph search represents a cornerstone in computer science and is employed when the best algorithmic solution to a problem consists in performing an analysis of a search space representing computational possibilities. Typically, in such problems it is crucial to determine the sequence of transitions performed that led to certain states. In this work we discuss how to adapt generic quantum search procedures, namely quantum random walks and Grover’s algorithm, in order to obtain computational paths. We then compare these approaches in the context of tree graphs. In addition we demonstrate that in a best-case scenario both approaches differ, performance-wise, by a constant factor speedup of two, whilst still providing a quadratic speedup relatively to their classical equivalents. We discuss the different scenarios that are better suited for each approach.

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 31, 2012

References

  • Quantum lower bounds by polynomials
    Beals, R.; Buhrman, H.; Cleve, R.; Mosca, M.; Wolf, R.

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