English

Quantum 3-SAT is QMA1-complete

Quantum Physics 2014-10-21 v1 Computational Complexity

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.

Cite

@article{arxiv.1302.0290,
  title  = {Quantum 3-SAT is QMA1-complete},
  author = {David Gosset and Daniel Nagaj},
  journal= {arXiv preprint arXiv:1302.0290},
  year   = {2014}
}
R2 v1 2026-06-21T23:19:28.446Z