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Algorithmica

, Volume 68, Issue 1, pp 152–189 | Cite as

Evolutionary Algorithms for Quantum Computers

  • Daniel Johannsen
  • Piyush P. Kurur
  • Johannes Lengler
Article
  • 393 Downloads

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.

Keywords

Theory Evolutionary computation Quantum algorithm Runtime analysis 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Johannsen
    • 1
  • Piyush P. Kurur
    • 2
  • Johannes Lengler
    • 3
  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Dept. of Comp. Sci. and Engg.Indian Institute of Technology KanpurKanpurIndia
  3. 3.Department of Theoretical Computer ScienceEidgenössische Technische Hochschule ETHZürichSwitzerland

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