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arXiv · 1302.0290

Quantum 3-SAT is QMA1-complete

David Gosset·Daniel Nagaj
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Abstract

Quantum satisfiability is a constraint satisfaction problem that generalizes classical boolean satisfiability. In the quantum k-SAT problem, each constraint is specified by a k-local projector and is satisfied by any state in its nullspace. Bravyi showed that quantum 2-SAT can be solved efficiently on a classical computer and that quantum k-SAT with k greater than or equal to 4 is QMA1-complete. Quantum 3-SAT was known to be contained in QMA1, but its computational hardness was unknown until now. We prove that quantum 3-SAT is QMA1-hard, and therefore complete for this complexity class.

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David Gosset, Daniel Nagaj. 2013-02-01. Quantum 3-SAT is QMA1-complete. https://doi.org/10.1109/focs.2013.86

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