  Entanglement forging based variational algorithms leverage the bi-partition
of quantum systems for addressing ground state problems. The primary limitation
of these approaches lies in the exponential summation required over the
numerous potential basis states, or bitstrings, when performing the Schmidt
decomposition of the whole system. To overcome this challenge, we propose a new
method for entanglement forging employing generative neural networks to
identify the most pertinent bitstrings, eliminating the need for the
exponential sum. Through empirical demonstrations on systems of increasing
complexity, we show that the proposed algorithm achieves comparable or superior
performance compared to the existing standard implementation of entanglement
forging. Moreover, by controlling the amount of required resources, this scheme
can be applied to larger, as well as non permutation invariant systems, where
the latter constraint is associated with the Heisenberg forging procedure. We
substantiate our findings through numerical simulations conducted on spins
models exhibiting one-dimensional ring, two-dimensional triangular lattice
topologies, and nuclear shell model configurations.
