表面码的一种有效马尔可夫链蒙特卡罗算法
An efficient Markov chain Monte Carlo algorithm for the surface code
摘要：
最小权重完美匹配（MWPM）已经是用于表面码中的错误校正的主要经典算法，因为它具有低运行时间复杂度并且实现相对低的逻辑错误率[Phys.Rev.Lett. 108，180501（2012）]。马尔可夫链蒙特卡罗（MCMC）算法[物理评论快报。109，160503（2012）]能够实现比MWPM更低的逻辑错误率和更高的阈值，但是需要经典的运行时复杂度，其是L（代码的线性大小）中的超多项式。在这项工作中，我们提出了一个MCMC算法，实现显着降低逻辑错误率比MWPM的成本多项式增加的经典运行时的复杂性。对于接近阈值的错误率p，我们的算法需要相对于MWPM增加O（L^2）的运行时复杂度，以实现较低的逻辑错误率。如果p低于依赖于L的临界值，则不再需要增加运行时复杂性。对于p->0，我们的算法实现的逻辑错误率是指数小于（在L）比MWPM，而不需要增加运行时的复杂性。我们的算法允许运行时间和实现的逻辑错误率以及并行化之间的权衡，也可以用来纠正不完美的稳定器测量的情况下。
英文摘要：
Minimum-weight perfect matching (MWPM) has been been the primary classical algorithm for error correction in the surface code, since it is of low runtime complexity and achieves relatively low logical error rates [Phys. Rev. Lett. 108, 180501 (2012)]. A Markov chain Monte Carlo (MCMC) algorithm [Phys. Rev. Lett. 109, 160503 (2012)] is able to achieve lower logical error rates and higher thresholds than MWPM, but requires a classical runtime complexity which is super-polynomial in L, the linear size of the code. In this work we present an MCMC algorithm that achieves significantly lower logical error rates than MWPM at the cost of a polynomially increased classical runtime complexity. For error rates p close to the threshold, our algorithm needs a runtime complexity which is increased by O(L^2) relative to MWPM in order to achieve a lower logical error rate. If p is below an L-dependent critical value, no increase in the runtime complexity is necessary any longer. For p->0, the logical error rate achieved by our algorithm is exponentially smaller (in L) than that of MWPM, without requiring an increased runtime complexity. Our algorithm allows for trade-offs between runtime and achieved logical error rates as well as for parallelization, and can be also used to correct in the case of imperfect stabilizer measurements.
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