Jastrow态和Stabilizer态的紧致神经网络量子态表示
Compact Neural-network Quantum State representations of Jastrow and Stabilizer states
摘要：
神经网络量子态（NQS）已成为多体物理研究的有力工具。在众多可能的架构中，神经网络可以编码量子态的振幅，限制玻尔兹曼机（RBM）的简单性已被证明对数值和分析研究特别有用。特别是为重要的状态类别（例如贾斯特罗和稳定态）设计精确的NQS表示，为了解基于RBM的NQS的优势和局限性提供了有用的线索。然而，$N$自旋系统的当前构造生成具有非常稀疏连接的$M \sim O(N^2)$隐藏单元的NQS。这使得它们与通常由数值优化生成的NQS相比是非典型的。在这里，我们专注于紧凑的NQS，表示具有隐藏单元密度$α= M/N \leq 1$但具有系统广泛的隐藏-可见单元连接的NQS。通过统一Jastrow和稳定状态，我们引入了一个新的精确表示，需要在最$M=N-1$隐藏单元，说明如何高度表达$α\leq 1$可以。由于其结构相似的数值NQS解决方案，我们的结果提供了有用的见解，并可能铺平道路，更多的家庭的量子态，以准确地表示紧凑的NQS。
英文摘要：
Neural-network quantum states (NQS) have become a powerful tool in many-body physics. Of the numerous possible architectures in which neural-networks can encode amplitudes of quantum states the simplicity of the Restricted Boltzmann Machine (RBM) has proven especially useful for both numerical and analytical studies. In particular devising exact NQS representations for important classes of states, like Jastrow and stabilizer states, has provided useful clues into the strengths and limitations of the RBM based NQS. However, current constructions for a system of $N$ spins generate NQS with $M \sim O(N^2)$ hidden units that are very sparsely connected. This makes them rather atypical NQS compared to those commonly generated by numerical optimisation. Here we focus on compact NQS, denoting NQS with a hidden unit density $α= M/N \leq 1$ but with system-extensive hidden-visible unit connectivity. By unifying Jastrow and stabilizer states we introduce a new exact representation that requires at most $M=N-1$ hidden units, illustrating how highly expressive $α\leq 1$ can be. Owing to their structural similarity to numerical NQS solutions our result provides useful insights and could pave the way for more families of quantum states to be represented exactly by compact NQS.
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