A Quantum Version of Schoening'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 this decision problem with high probability for n qubits, L clauses, and promise gap c in time O(n[superscript 2]L[superscript 2]c[superscript −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.