We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. We show how to use our method to analyze hypothetical quantum computers with various configurations and select designs with lower error rates. Currently, this requires expensive classical simulations of quantum decoders for various distances and physical error rates or inaccurate extrapolation from minimal experimental data. Instead, we use the symmetry of the problem to count the configurations that result in a logical error with our novel software. Given a physical error rate, we can deduce the probability of a logical error, to provably good accuracy. We include an analysis of measurement errors to allow a more complete comparison of different surface code implementations.

翻译：我们提出了一种新颖的方法来计算表面码中的逻辑错误率，假设物理错误是独立同分布的。我们展示了如何使用该方法分析不同配置的假想量子计算机，并选择具有更低错误率的设计。目前，这需要针对各种距离和物理错误率进行昂贵的量子解码器经典模拟，或根据最小实验数据进行不准确的外推。相反，我们利用问题的对称性，通过新开发的软件统计导致逻辑错误的配置。给定物理错误率，我们可以推导出逻辑错误的概率，并保证可证明的准确性。我们还包含了对测量误差的分析，以便更全面地比较不同的表面码实现。