Quantum Answer Set Programming Solver Using Amplitude Amplification

In this paper, a Quantum Answer set programming solver (QASP) will be proposed to solve NP-hard combinatorial search problems. The paper shows that problems such as Hamiltonian cycle problem and N-queen problem encoded as ASP can be reduced to a MAX-3-SAT problem in a 3-CNF form. The 3-CNF Boolean formula will be solved using the proposed quantum solver with
$O(n+ m)$
qubits where
$n$
is the input variables number,
$m$
is the clauses number in
$O(\sqrt{2^{n/m}})$
steps.