TY - GEN

T1 - Solving NP-complete problems with quantum search

AU - Fürer, Martin

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-540-78773-0_67

DO - 10.1007/978-3-540-78773-0_67

M3 - Conference contribution

AN - SCOPUS:43049149787

SN - 3540787720

SN - 9783540787723

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 784

EP - 792

BT - LATIN 2008

T2 - 8th Latin American TheoreticalINformatics Symposium, LATIN 2008

Y2 - 7 April 2008 through 11 April 2008

ER -