Compact neural-network quantum state representations of Jastrow and stabilizer states

Neural-network quantum states (NQS) have become a powerful tool in many-body physics. Of the numerous possible architectures which neural-networks can encode amplitudes of simplicity Restricted Boltzmann Machine (RBM) has proven especially useful for both numerical and analytical studies. In particular devising exact NQS representations important classes states, like Jastrow stabilizer provided clues into strengths limitations RBM based NQS. However, current constructions system $N$ spins generate with $M \sim O(N^2)$ hidden units that are very sparsely connected. This makes them rather atypical compared to those commonly generated by optimisation. Here we focus on compact NQS, denoting unit density $\alpha = M/N \leq 1$ but system-extensive hidden-visible connectivity. By unifying introduce new representation requires at most $M=N-1$ units, illustrating how highly expressive be. Owing their structural similarity solutions our result provides insights could pave way more families be represented exactly