Quantum computing shows great potential, but errors pose a significant
challenge. This study explores new strategies for mitigating quantum errors
using artificial neural networks (ANN) and the Yang-Baxter equation (YBE).
Unlike traditional error correction methods, which are computationally
intensive, we investigate artificial error mitigation. The manuscript
introduces the basics of quantum error sources and explores the potential of
using classical computation for error mitigation. The Yang-Baxter equation
plays a crucial role, allowing us to compress time dynamics simulations into
constant-depth circuits. By introducing controlled noise through the YBE, we
enhance the dataset for error mitigation. We train an ANN model on partial data
from quantum simulations, demonstrating its effectiveness in correcting errors
in time-evolving quantum states.

量子计算显示出巨大的潜力，但错误会带来重大挑战。本研究探索了使用人工神经网络（ANN）和杨 - 巴克斯特方程（YBE）减轻量子错误的新策略。与传统的计算密集型纠错方法不同，我们研究了人工错误调节。该文介绍了量子错误来源的基本知识，并探索了使用经典计算进行错误调节的潜力。杨 - 巴克斯特方程起着关键作用，使我们能够将时间动力学模拟压缩成恒定深度电路。通过在 YBE 中引入受控噪声，我们增强了用于错误调节的数据集。我们在量子模拟的部分数据上训练了一个 ANN 模型，证明了它在纠正时间演化的量子态中的错误方面的有效性。

用杨 - 巴克斯特方程和人工神经网络介导的量子错误缓解和校正

Quantum error mitigation and correction mediated by Yang-Baxter equation  and artificial neural network

We provide a novel Neural Network architecture that can: i) output R-matrix
for a given quantum integrable spin chain, ii) search for an integrable
Hamiltonian and the corresponding R-matrix under assumptions of certain
symmetries or other restrictions, iii) explore the space of Hamiltonians around
already learned models and reconstruct the family of integrable spin chains
which they belong to. The neural network training is done by minimizing loss
functions encoding Yang-Baxter equation, regularity and other model-specific
restrictions such as hermiticity. Holomorphy is implemented via the choice of
activation functions. We demonstrate the work of our Neural Network on the
two-dimensional spin chains of difference form. In particular, we reconstruct
the R-matrices for all 14 classes. We also demonstrate its utility as an
\textit{Explorer}, scanning a certain subspace of Hamiltonians and identifying
integrable classes after clusterisation. The last strategy can be used in
future to carve out the map of integrable spin chains in higher dimensions and
in more general settings where no analytical methods are available.

本研究提出了一种新颖的神经网络结构，可以用于输出给定量子可积自旋链的 R - 矩阵，搜索对称性或其他限制条件下的可积哈密顿量和相应的 R - 矩阵，以及探索已学习模型周围哈密顿量的空间并重构它们所属的自旋链族。