用受限玻尔兹曼机表示环面码的任意基态
Representing arbitrary ground states of toric code by a restricted Boltzmann machine
AI总结：
本文系统分析了受限玻尔兹曼机表示环面码基态的能力，并通过引入非局部连接提出可解析求解的新模型，将其从 $Z_2$ 推广到 $Z_n$ 环面码。
摘要：
我们系统地分析了环面码基态在仅具有隐藏神经元与可见神经元之间局部连接的受限玻尔兹曼机（Restricted Boltzmann Machine）下的可表示性。这一分析对于评估该模型表示不同基态的能力至关重要，从而加深我们对其优势与局限的理解。随后，我们通过高效地引入必要的非局部连接，对受限玻尔兹曼机进行了修改，以容纳任意基态。新模型不仅可解析求解，而且在利用机器学习技术求解时展现出高效且准确的性能。然后，我们将模型从 $Z_2$ 环面码推广到 $Z_n$ 环面码，并讨论了未来的研究方向。
英文摘要：
We systematically analyze the representability of toric code ground states by Restricted Boltzmann Machine with only local connections between hidden and visible neurons. This analysis is pivotal for evaluating the model's capability to represent diverse ground states, thus enhancing our understanding of its strengths and weaknesses. Subsequently, we modify the Restricted Boltzmann Machine to accommodate arbitrary ground states by introducing essential non-local connections efficiently. The new model is not only analytically solvable but also demonstrates efficient and accurate performance when solved using machine learning techniques. Then we generalize our the model from $Z_2$ to $Z_n$ toric code and discuss future directions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
