A Quantum Version of Sch\"oning's Algorithm Applied to Quantum 2-SAT
Quantum Physics
2016-03-24 v1 Computational Complexity
Data Structures and Algorithms
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^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.
Keywords
Cite
@article{arxiv.1603.06985,
title = {A Quantum Version of Sch\"oning's Algorithm Applied to Quantum 2-SAT},
author = {Edward Farhi and Shelby Kimmel and Kristan Temme},
journal= {arXiv preprint arXiv:1603.06985},
year = {2016}
}