The paper "Augmenting Density Matrix Renormalization Group with Clifford Circuits" by Xiangjian Qian, Jiale Huang, and Mingpu Qin explores the integration of Clifford circuits into the Density Matrix Renormalization Group (DMRG) algorithm to enhance the simulation of two-dimensional (2D) quantum many-body systems. DMRG and Matrix Product States (MPS) are effective methods for studying one-dimensional systems but face challenges when applied to 2D systems due to the limited entanglement in the wave-function ansatz. Clifford circuits, which can generate highly entangled but simulable states, offer a promising solution. The authors propose a new Tensor Network ansatz called CAMPS (Clifford Circuits Augmented MPS), which incorporates additional Clifford circuits into the MPS framework. This approach maintains the same computational complexity as MPS while significantly improving simulation accuracy. Numerical simulations on the 2D $J_1 - J_2$ Heisenberg model demonstrate that CAMPS achieves a relative error of order $10^{-4}$ with a bond dimension of $D \approx 1000$, outperforming pure MPS calculations. The study highlights the potential of CAMPS in unraveling the complexities of 2D quantum systems and suggests its adaptability to other numerical simulation methods.The paper "Augmenting Density Matrix Renormalization Group with Clifford Circuits" by Xiangjian Qian, Jiale Huang, and Mingpu Qin explores the integration of Clifford circuits into the Density Matrix Renormalization Group (DMRG) algorithm to enhance the simulation of two-dimensional (2D) quantum many-body systems. DMRG and Matrix Product States (MPS) are effective methods for studying one-dimensional systems but face challenges when applied to 2D systems due to the limited entanglement in the wave-function ansatz. Clifford circuits, which can generate highly entangled but simulable states, offer a promising solution. The authors propose a new Tensor Network ansatz called CAMPS (Clifford Circuits Augmented MPS), which incorporates additional Clifford circuits into the MPS framework. This approach maintains the same computational complexity as MPS while significantly improving simulation accuracy. Numerical simulations on the 2D $J_1 - J_2$ Heisenberg model demonstrate that CAMPS achieves a relative error of order $10^{-4}$ with a bond dimension of $D \approx 1000$, outperforming pure MPS calculations. The study highlights the potential of CAMPS in unraveling the complexities of 2D quantum systems and suggests its adaptability to other numerical simulation methods.