Ground state energy: Can it really be reached with quantum annealers?
Finding the ground state energy of a Hamiltonian $H$, which describes a quantum system of several interacting subsystems, is crucial as well for many-body physics as for various optimization problems. Variety of algorithms and simulation procedures (either hardware or software based) rely on the separability approximation, in which one seeks for the minimal expectation value of $H$ among all product states. We demonstrate that already for systems with nearest neighbor interactions this approximation is inaccurate, which implies fundamental restrictions for precision of computations performed with near-term quantum annealers. Furthermore, for generic Hamiltonians this approximation leads to significant systematic errors as the minimal expectation value among separable states asymptotically tends to zero. As a result, we introduce an effective entanglement witness based on a generic observable that is applicable for any multipartite quantum system.