Title: Clifford Circuits Augmented Time-Dependent Variational Principle Show Chinese title

Title: Clifford 电路增强的时间依赖变分原理

Abstract: The recently proposed Clifford Circuits Augmented Matrix Product States (CA-MPS) (arXiv:2405.09217) seamlessly augments Density Matrix Renormalization Group with Clifford circuits. In CA-MPS, the entanglement from stabilizers is transferred to the Clifford circuits which can be easily handled according to the Gottesman-Knill theorem. As a result, MPS needs only to deal with the non-stabilizer entanglement, which largely reduce the bond dimension and the resource required for the accurate simulation of many-body systems. In this work, we generalize CA-MPS to the framework of Time-Dependent Variational Principle (TDVP) for time evolution simulations. In this method, we apply Clifford circuits to the resulting MPS in each TDVP step with a two-site sweeping process similar as in DMRG, aiming at reducing the entanglement entropy in the MPS, and the Hamiltonian is transformed accordingly using the chosen Clifford circuits. Similar as in CA-MPS, the Clifford circuits doesn't increase the number of terms in the Hamiltonian which makes the overhead very small in the new method. We test this method in both XXZ chain and two dimensional Heisenberg model. The results show that the Clifford circuits augmented TDVP method can reduce the entanglement entropy in the time evolution process and hence makes the simulation reliable for longer time. The Clifford circuits augmented Time-Dependent Variational Principle provides a useful tool for the simulation of time evolution process of many-body systems in the future. Show Chinese abstract

Abstract: 最近提出的克利福德电路增强矩阵乘积态（CA-MPS）（arXiv:2405.09217）无缝地将密度矩阵重整化群与克利福德电路结合在一起。 在CA-MPS中，来自稳定子的纠缠被转移到克利福德电路中，根据戈特沙尔克-尼兰定理，这可以很容易地处理。 因此，矩阵乘积态（MPS）只需要处理非稳定子的纠缠，这大大减少了多体系统精确模拟所需的边界维度和资源。 在这项工作中，我们将CA-MPS推广到时间相关变分原理（TDVP）的时间演化模拟框架中。 在此方法中，我们在每个TDVP步骤中应用克利福德电路到产生的MPS上，采用类似于DMRG的两站点扫描过程，目的是减少MPS中的纠缠熵，并相应地使用选定的克利福德电路变换哈密顿量。 与CA-MPS类似，克利福德电路不会增加哈密顿量中的项数，这使得新方法的开销非常小。 我们在这两种情况下测试了这种方法：XXZ链和二维海森堡模型。 结果显示，克利福德电路增强的TDVP方法可以减少时间演化过程中的纠缠熵，从而使更长时间的模拟变得可靠。 克利福德电路增强的时间相关变分原理为未来多体系统时间演化过程的模拟提供了一个有用的工具。