论文标题
复曲面代码和X-Cube Fracton模型的量子电路
Quantum circuits for toric code and X-cube fracton model
论文作者
论文摘要
我们提出了一个系统，有效的量子电路，该电路仅由Clifford门组成，用于模拟表面代码模型的基态。该方法在$ \ lceil 2l+2+log_ {2}（d）+\ frac {l} {l} {2d} \ rceil $ time步骤中产生圆环代码的基态状态，其中$ l $表示系统大小，$ d $代表约束Cnot Gates的最大距离。我们的算法将问题重新制定为纯粹的几何形状，促进了其扩展以达到某些3D拓扑阶段的基础状态，例如$ 3L+8 $步骤的3D折叠模型和$ 12L+11美元的X-Cube Fracton模型。此外，我们引入了一种涉及测量值的胶合方法，使我们的技术能够在任意平面晶格上达到2D旋转法规的基态，并为更复杂的3D拓扑阶段铺平了道路。
We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $\lceil 2L+2+log_{2}(d)+\frac{L}{2d} \rceil$ time steps, where $L$ refers to the system size and $d$ represents the maximum distance to constrain the application of the CNOT gates. Our algorithm reformulates the problem into a purely geometric one, facilitating its extension to attain the ground state of certain 3D topological phases, such as the 3D toric model in $3L+8$ steps and the X-cube fracton model in $12L+11$ steps. Furthermore, we introduce a gluing method involving measurements, enabling our technique to attain the ground state of the 2D toric code on an arbitrary planar lattice and paving the way to more intricate 3D topological phases.
