  The optimal use of quantum and classical computational techniques together is
important to address problems that cannot be easily solved by quantum
computations alone. This is the case of the ground state problem for quantum
many-body systems. We show here that probabilistic generative models can work
in conjunction with quantum algorithms to design hybrid quantum-classical
variational ans\"atze that forge entanglement to lower quantum resource
overhead. The variational ans\"atze comprise parametrized quantum circuits on
two separate quantum registers, and a classical generative neural network that
can entangle them by learning a Schmidt decomposition of the whole system. The
method presented is efficient in terms of the number of measurements required
to achieve fixed precision on expected values of observables. To demonstrate
its effectiveness, we perform numerical experiments on the transverse field
Ising model in one and two dimensions, and fermionic systems such as the t-V
Hamiltonian of spinless fermions on a lattice.
