Efficient algorithm for a quantum analogue of 2-SAT

Abstract

Complexity of a quantum analogue of the satisfiability problem is studied. Quantum k-SAT is a problem of verifying whether there exists n-qubit pure state such that its k-qubit reduced density matrices have support on prescribed subspaces. We present a classical algorithm solving quantum 2-SAT in a polynomial time. It generalizes the well-known algorithm for the classical 2-SAT. Besides, we show that for any k>=4 quantum k-SAT is complete in the complexity class QMA with one-sided error.