标题： 用量子张量列车求解Gross-Pitaevskii方程：基态和非线性动力学 显示英文标题

标题： Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics

摘要： 我们开发了一个基于量子张量列车(QTT)格式的张量网络框架，以高效求解描述平均场理论下玻色-爱因斯坦凝聚体的格罗斯-皮塔耶夫斯基方程(GPE)。通过适应时间依赖变分原理(TDVP)和梯度下降方法，我们在QTT结构内准确处理GPE的非线性。我们的方法实现了高分辨率模拟，并大幅降低了计算成本。我们对BEC的基态和动力学进行了基准测试——包括涡旋晶格形成和呼吸模式——展示了优于传统网格方法的性能，并由于饱和的键维数实现了稳定的长时间演化。这确立了QTT作为非线性量子模拟的强大工具。 显示英文摘要

摘要： We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent variational principle (TDVP) and gradient descent methods, we accurately handle the GPE's nonlinearities within the QTT structure. Our approach enables high-resolution simulations with drastically reduced computational cost. We benchmark ground states and dynamics of BECs--including vortex lattice formation and breathing modes--demonstrating superior performance over conventional grid-based methods and stable long-time evolution due to saturating bond dimensions. This establishes QTT as a powerful tool for nonlinear quantum simulations.