论文标题
通过三维表面代码在新型晶格切片中的及时解码的数值实现
Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code
论文作者
论文摘要
我们基于B. Brown（Sci。Adv。6，EAAY4929（2020））的最新工作，以开发和模拟三种3D表面代码中的即时解码方案的明确配方，该方案可用于在三个2D表面编码之间实现Transersersal（non-Clifford）$ \ overline $ \ interline $ \ overline {ccz} $。我们通过3D代码提供了一组详细的有界高架切片集，该切片保留了整个3D代码的代码距离和测量误差检测属性，并接纳了一个尺寸跳跃的过程，该过程从/折叠到每个切片边界上支持的2D表面代码。在该过程的每个时间步中，切片在一组普通的重叠QCZ $上都应应用$ ccz $的普通量子。我们使用这些切片来模拟对随机$ x $的简单JIT解码器的性能和测量错误，并在所有三个代码中找到阈值$ p_c \ sim 0.1 \％$的证据。我们希望通过优化解码器来改善此阈值。
We build on recent work by B. Brown (Sci. Adv. 6, eaay4929 (2020)) to develop and simulate an explicit recipe for a just-in-time decoding scheme in three 3D surface codes, which can be used to implement a transversal (non-Clifford) $\overline{CCZ}$ between three 2D surface codes in time linear in the code distance. We present a fully detailed set of bounded-height lattice slices through the 3D codes which retain the code distance and measurement-error detecting properties of the full 3D code and admit a dimension-jumping process which expands from/collapses to 2D surface codes supported on the boundaries of each slice. At each timestep of the procedure the slices agree on a common set of overlapping qubits on which $CCZ$ should be applied. We use these slices to simulate the performance of a simple JIT decoder against stochastic $X$ and measurement errors and find evidence for a threshold $p_c \sim 0.1\%$ in all three codes. We expect that this threshold could be improved by optimisation of the decoder.
