A quantum version of Schoning's algorithm applied to quantum 2-SAT
Edward Farhi, Shelby Kimmel, Kristan Temme · Quantum Information and Computation · 2016
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 these decision problems 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 Schoning’s probabilistic algorithm for k-SAT.