Solving NP-complete problems with quantum search

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    4 Scopus citations

    Abstract

    In his seminal paper, Grover points out the prospect of faster solutions for an NP-complete problem like SAT. If there are n variables, then an obvious classical deterministic algorithm checks out all 2 n truth assignments in about 2 n steps, while his quantum search algorithm can find a satisfying truth assignment in about 2 n/2 steps. For several NP-complete problems, many sophisticated classical algorithms have been designed. They are still exponential, but much faster than the brute force algorithms. The question arises whether their running time can still be decreased from T(n) to by using a quantum computer. Isolated positive examples are known, and some speed-up has been obtained for wider classes. Here, we present a simple method to obtain the full T(n) to speed-up for most of the many non-trivial exponential time algorithms for NP-hard problems. The method works whenever the widely used technique of recursive decomposition is employed. This included all currently known algorithms for which such a speed-up has not yet been known.

    Original languageEnglish (US)
    Title of host publicationLATIN 2008
    Subtitle of host publicationTheoretical Informatics - 8th Latin American Symposium, Proceedings
    Pages784-792
    Number of pages9
    DOIs
    StatePublished - May 12 2008
    Event8th Latin American TheoreticalINformatics Symposium, LATIN 2008 - Buzios, Brazil
    Duration: Apr 7 2008Apr 11 2008

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume4957 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other8th Latin American TheoreticalINformatics Symposium, LATIN 2008
    CountryBrazil
    CityBuzios
    Period4/7/084/11/08

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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