A quantum version of Schöning’s algorithm applied to Quantum 2-SAT

Abstract

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(n2L2c−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 Schöning’s probabilistic algorithm for k-SAT.