Quantum 3-SAT is QMA1-complete

TL;DR

This paper proves that quantum 3-SAT is QMA1-complete, establishing its computational hardness and completing the classification of quantum k-SAT problems for k ≥ 3.

Contribution

The paper demonstrates that quantum 3-SAT is QMA1-hard, filling a gap in understanding its complexity and confirming its status as QMA1-complete.

Findings

Quantum 3-SAT is QMA1-hard.

Quantum 3-SAT is contained in QMA1, thus QMA1-complete.

Completes the complexity classification of quantum k-SAT for k ≥ 3.

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.