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arXiv · 1603.06985

A Quantum Version of Sch\"oning's Algorithm Applied to Quantum 2-SAT

Edward Farhi·Shelby Kimmel·Kristan Temme
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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.

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Edward Farhi, Shelby Kimmel, Kristan Temme. 2016-03-22. A Quantum Version of Sch\"oning's Algorithm Applied to Quantum 2-SAT. https://arxiv.org/abs/1603.06985

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