Evolutionary Algorithms for Quantum Computers
OPEN ACCESS
Author / Producer
Date
2014-01
Publication Type
Journal Article
ETH Bibliography
yes
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OPEN ACCESS
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Abstract
In this article, we formulate and study quantum analogues of randomized search heuristics, which make use of Grover search (in Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 212–219. ACM, New York, 1996) to accelerate the search for improved offsprings. We then specialize the above formulation to two specific search heuristics: Random Local Search and the (1+1) Evolutionary Algorithm. We call the resulting quantum versions of these search heuristics Quantum Local Search and the (1+1) Quantum Evolutionary Algorithm.
We conduct a rigorous runtime analysis of these quantum search heuristics in the computation model of quantum algorithms, which, besides classical computation steps, also permits those unique to quantum computing devices. To this end, we study the six elementary pseudo-Boolean optimization problems OneMax, LeadingOnes, Discrepancy, Needle, Jump, and TinyTrap.
It turns out that the advantage of the respective quantum search heuristic over its classical counterpart varies with the problem structure and ranges from no speedup at all for the problem Discrepancy to exponential speedup for the problem TinyTrap. We show that these runtime behaviors are closely linked to the probabilities of performing successful mutations in the classical algorithms.
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Publication status
published
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Editor
Book title
Journal / series
Volume
68 (1)
Pages / Article No.
152 - 189
Publisher
Springer
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Theory; Evolutionary computation; Quantum algorithm; Runtime analysis
Organisational unit
03672 - Steger, Angelika (emeritus) / Steger, Angelika (emeritus)
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.