AI 中文总结
该研究针对高维抛物型偏微分方程求解问题，提出基于多层全连接变分量子电路的量子变压器BSDE求解器，通过将归一化状态轨迹视为令牌并应用因果自注意力学习相互作用，实验表明该方法在特定条件下有效。
AI 中文摘要
求解高维抛物型偏微分方程在工程、物理和随机控制中具有重要意义。深度倒向随机微分方程（BSDE）方法将半线性偏微分方程重新表述为倒向随机微分方程，并具有基于模型的强化学习解释。我们提出了一种基于多层全连接变分量子电路（FC-VQC）的量子变压器BSDE求解器。该方法将归一化状态轨迹视为时间坐标令牌，并应用因果自注意力来学习适配的BSDE梯度过程中的相互作用。所有可训练模型参数都包含在FC-VQC的嵌入、投影、前馈和解码器模块中，而注意力和结构操作保持经典且无参数。在三个d = 36的偏微分方程基准上的实验表明，QTransformer始终优于非注意力FC-VQC基线，并且在紧凑隐藏宽度下优于经典变压器，而更宽的经典变压器实现了最佳的整体精度。这些结果表明，将因果注意力与FC-VQC相结合为高维BSDE轨迹学习提供了一种有效的量子架构。
英文摘要
Solving high-dimensional parabolic partial differential equations (PDEs) is important in engineering, physics, and stochastic control. Deep BSDE methods reformulate semilinear PDEs as backward stochastic differential equations and admit a model-based reinforcement learning interpretation, where trajectories are generated from known stochastic dynamics while a trainable model learns the gradient-related control process. We propose a Quantum Transformer BSDE solver based on Multi-Layer Fully-Connected Variational Quantum Circuits (FC-VQC). The method treats the normalized state trajectory as time--coordinate tokens and applies causal self-attention to learn interactions in the adapted BSDE gradient process. All trainable model parameters are contained within the FC-VQC embedding, projection, feed-forward, and decoder modules, while attention and structural operations remain classical and parameter-free. Experiments on three d=36 PDE benchmarks show that QTransformer consistently improves over the non-attentive FC-VQC baseline and outperforms the classical Transformer at compact hidden widths, while the wider classical Transformer achieves the best overall accuracy. These results demonstrate that combining causal attention with FC-VQC provides an effective quantum architecture for high-dimensional BSDE trajectory learning.
Comments4 pages, 2 figures
