论文标题
三维同源产品代码的单次误差校正
Single-shot error correction of three-dimensional homological product codes
论文作者
论文摘要
单次误差校正仅使用一轮噪声测量值纠正数据噪声，从而消除了对密集测量重复的需求。我们介绍了量子代码限制的一般概念，该量子代码大致规定量子误差不会触发更多的测量综合症。我们证明，限制足以使对抗误差的单次解码，线性限制足以单发局部随机误差。除此之外，我们证明了所有三维同源产品代码在其$ x $ - 组件中均显示出限制，因此对于对抗性相纤维噪声而言是单一的。对于局部随机相叉噪声，我们从数值探索这些代码，并再次找到单次保护的证据。我们的蒙特卡洛模拟表明3D表面和感谢您的3D表面和福利码的可持续性阈值分别为$ 3.08（4）\％$和$ 2.90（2）\％$，这是迄今为止观察到的最高单发阈值。为了展示超出拓扑代码类别的单次误差校正，我们还对随机构造的3D同源产品代码进行了模拟。
Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes, which roughly stipulates qubit errors cannot grow without triggering more measurement syndromes. We prove confinement is sufficient for single-shot decoding of adversarial errors and linear confinement is sufficient for single-shot decoding of local stochastic errors. Further to this, we prove that all three-dimensional homological product codes exhibit confinement in their $X$-components and are therefore single-shot for adversarial phase-flip noise. For local stochastic phase-flip noise, we numerically explore these codes and again find evidence of single-shot protection. Our Monte Carlo simulations indicate sustainable thresholds of $3.08(4)\%$ and $2.90(2)\%$ for 3D surface and toric codes respectively, the highest observed single-shot thresholds to date. To demonstrate single-shot error correction beyond the class of topological codes, we also run simulations on a randomly constructed 3D homological product code.
