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Published October 2016 | Submitted
Journal Article Open

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.

Additional Information

© 2016 Rinton Press. We thank Sevag Gharibian for helpful discussions. EF was funded by NSF grant CCF-1218176 and ARO contract W911NF-12-1-0486. SK acknowledges support from the Department of Physics at MIT, iQuISE Igert grant contract number DGE-0801525, and the Department of Defense. KT acknowledges the support from the Erwin Schrödinger fellowship, Austrian Science Fund (FWF): J 3219-N16 and funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NFS Grants PHY-1125565 and PHY-0803371) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).

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August 20, 2023
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