Solving NP-Complete Problems with Quantum Search

  • Martin Fürer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4957)


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 \(\tilde{O}(\sqrt{T(n)})\) 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Martin Fürer
    • 1
  1. 1.Department of Computer Science and EngineeringPennsylvania State UniversityUSA

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