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Latin American Symposium on Theoretical Informatics

LATIN 2008: LATIN 2008: Theoretical Informatics pp 784–792Cite as

Solving NP-Complete Problems with Quantum Search

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4957))

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 2n truth assignments in about 2n steps, while his quantum search algorithm can find a satisfying truth assignment in about 2n/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 \(\tilde{O}(\sqrt{T(n)})\) 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 \(\tilde{O}(\sqrt{T(n)})\) 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.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Pennsylvania State University, University Park, PA 16802, USA

    Martin Fürer

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  1. Martin Fürer
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Editor information

Eduardo Sany Laber Claudson Bornstein Loana Tito Nogueira Luerbio Faria

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Fürer, M. (2008). Solving NP-Complete Problems with Quantum Search. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_67

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  • DOI: https://doi.org/10.1007/978-3-540-78773-0_67

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78772-3

  • Online ISBN: 978-3-540-78773-0

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