01010nas a2200145 4500008004100000245007200041210006800113260001500181490000700196520056900203100001800772700001900790700001900809856003600828 2016 eng d00aA Quantum Version of Schöning's Algorithm Applied to Quantum 2-SAT0 aQuantum Version of Schönings Algorithm Applied to Quantum 2SAT c2016/03/220 v163 a
We study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves this decision problem with high probability for n qubits, L clauses, and promise gap c in time O(n^2 L^2 c^{-2}). If the Hamiltonian is additionally polynomially gapped, our algorithm efficiently produces a state that has high overlap with the satisfying subspace. The Markov process we study is a quantum analogue of Sch\"oning's probabilistic algorithm for k-SAT.
1 aFarhi, Edward1 aKimmel, Shelby1 aTemme, Kristan uhttp://arxiv.org/abs/1603.06985