We study the computational complexity of the $N$-representability problem in quantum chemistry. We show that this problem is quantum Merlin-Arthur complete, which is the quantum generalization of nondeterministic polynomial time complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that reduces the problem of finding ground states to $N$ representability.

• Received 17 September 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.110503