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.

翻译：基于纠缠锻造的变分算法利用量子系统的二分法来解决基态问题。这些方法的主要局限在于，在对整个系统进行施密特分解时，需要对大量潜在基态（即比特串）进行指数级求和。为克服这一挑战，我们提出了一种新的纠缠锻造方法，该方法采用生成式神经网络来识别最相关的比特串，从而消除了指数求和的需求。通过在复杂度逐步提升的系统上进行实证演示，我们表明，与现有标准纠缠锻造实现相比，所提算法实现了相当或更优的性能。此外，通过控制所需资源量，该方案可应用于更大规模以及非置换不变系统——后者与海森堡锻造过程相关的约束有关。我们通过数值模拟证实了研究结果，模拟对象包括呈现一维环状拓扑、二维三角晶格拓扑的自旋模型以及原子核壳层模型构型。