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Entanglement forging based variational algorithms leverage the bi-partitionof quantum systems for addressing ground state problems. The primary limitationof these approaches lies in the exponential summation required over thenumerous potential basis states, or bitstrings, when performing the Schmidtdecomposition of the whole system. To overcome this challenge, we propose a newmethod for entanglement forging employing generative neural networks toidentify the most pertinent bitstrings, eliminating the need for theexponential sum. Through empirical demonstrations on systems of increasingcomplexity, we show that the proposed algorithm achieves comparable or superiorperformance compared to the existing standard implementation of entanglementforging. Moreover, by controlling the amount of required resources, this schemecan be applied to larger, as well as non permutation invariant systems, wherethe latter constraint is associated with the Heisenberg forging procedure. Wesubstantiate our findings through numerical simulations conducted on spinsmodels exhibiting one-dimensional ring, two-dimensional triangular latticetopologies, and nuclear shell model configurations.

Hybrid Ground-State Quantum Algorithms based on Neural Schr\"odinger Forging