Quantum cooperative search algorithm for 3-SAT

Miguel A. Hernández Barreto, Gonzalo Abal, Sergio Nesmachnow

Abdesslem Layeb, Djamel Eddine Saïdouni

Tad Hogg

A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for which the generalized algorithm can find a solution in a constant number of steps as the number of variables increases. This performance contrasts with the linear growth in the number of steps required by the best classical algorithms, and the exponential number required by classical and quantum methods that ignore the problem structure. In some cases, the algorithm can also guarantee that insoluble problems in fact have no solutions, unlike previously proposed quantum search algorithms.

Charles Varmantchaonala Moudina, Jean Louis Ebongue Kedieng Fendji, J.-P. Tchapet Njafa +1 more

Charles Varmantchaonala Moudina, Jean Louis Ebongue Kedieng Fendji, J.-P. Tchapet Njafa +1 more

Evgeny Yakovlevich Dantsin, Владик Крейнович, Alexander Wolpert

It is well known that a straightforward application of Grover's quantum search algorithm enables to solve SAT in O (2 n /2 ) steps. Ambainis (SIGACT News, 2004) observed that it is possible to use Grover's technique to similarly speed up a sophisticated algorithm for solving 3-SAT. In this note, we show that a similar speed up can be obtained for all major record-breaking algorithms for satisfiability. We also show that if we use Grover's technique only, then we cannot do better than quadratic speed up.