论文标题
部分可观测时空混沌系统的无模型预测
A Pair Measurement Surface Code on Pentagons
论文作者
论文摘要
在本文中，我提出了一种将表面代码编译成两体奇偶校验测量（“配对测量”）的方法，其中一对测量沿开罗五边形瓷砖的边缘运行。 Chao等人的先前工作改善了所得电路。通过使用每个四体稳定器测量（5而不是6个），每轮稳定器测量的时间步长更少（6而不是10），则使用较少的对测量值。使用Monte Carlo抽样，我表明这些改进将表面代码的阈值从$ \ \ \％$ \％$ \ $ \ $ \％$ \％$ $ \％$ $ \％$ \％$ 0.1 \％$ $ \％的$ \ y $ \ y $ \ y $ \ qubit。但是，我还表明，随着物理错误率的降低，Chao等人的结构的Teraquop足迹比矿山的速度更快，并且可能低于$ \ $ \ 0.03 \％$的物理门错误率（由于我的构造中的双向挂钩错误）。我还与平面蜂窝代码进行了比较，表明，尽管这项工作确实会明显减少表面代码和蜂窝代码之间的差距（当汇编成对测量值时），但蜂窝代码仍然更有效（阈值$ \％\％\％$，teraquop footprint，teraquop footprint，teraquop footprint tera $ 0.1 \％$ of 0.1 \％$ of $ $ \ of $ \ about $ \ about $）。
In this paper, I present a way to compile the surface code into two-body parity measurements ("pair measurements"), where the pair measurements run along the edges of a Cairo pentagonal tiling. The resulting circuit improves on prior work by Chao et al. by using fewer pair measurements per four-body stabilizer measurement (5 instead of 6) and fewer time steps per round of stabilizer measurement (6 instead of 10). Using Monte Carlo sampling, I show that these improvements increase the threshold of the surface code when compiling into pair measurements from $\approx 0.2\%$ to $\approx 0.4\%$, and also that they improve the teraquop footprint at a $0.1\%$ physical gate error rate from $\approx6000$ qubits to $\approx3000$ qubits. However, I also show that the teraquop footprint of Chao et al's construction improves more quickly than mine as physical error rate decreases, and is likely better below a physical gate error rate of $\approx 0.03\%$ (due to bidirectional hook errors in my construction). I also compare to the planar honeycomb code, showing that although this work does noticeably reduce the gap between the surface code and the honeycomb code (when compiling into pair measurements), the honeycomb code is still more efficient (threshold $\approx 0.8\%$, teraquop footprint at $0.1\%$ of $\approx 1000$).
