Title: Competing automorphisms and disordered Floquet codes Show Chinese title

Title: 竞争自同构和无序Floquet码

Abstract: Topological order is a promising basis for quantum error correction, a key milestone towards large-scale quantum computing. Floquet codes provide a dynamical scheme for this while also exhibiting Floquet-enriched topological order (FET) where anyons periodically undergo a measurement-induced automorphism that acts uniformly in space. We study disordered Floquet codes where automorphisms have a spatiotemporally heterogeneous distribution -- the automorphisms "compete". We characterize the effect of this competition, showing how key features of the purification dynamics of mixed codestates can be inferred from anyon and automorphism properties for any Abelian topological order. This perspective can explain the protection or measurement of logical information in a dynamic automorphism (DA) code when subjected to a noise model of missing measurements. We demonstrate this using a DA color code with perturbed measurement sequences. The framework of competing automorphisms captures essential features of Floquet codes and robustness to noise, and may elucidate key mechanisms involving topological order, automorphisms, and fault-tolerance. Show Chinese abstract

Abstract: 拓扑序是一种有前景的量子纠错基础，这是迈向大规模量子计算的关键里程碑。 Floquet码为此提供了一个动态方案，同时表现出Floquet富集的拓扑序（FET），其中任意子会周期性地经历一种由测量诱导的自同构，该自同构在空间上均匀作用。 我们研究了无序的Floquet码，其中自同构具有时空异质分布——这些自同构“相互竞争”。 我们表征了这种竞争的影响，展示了如何从任意子和自同构的属性推断出任意阿贝尔拓扑序混合码字纯化动力学的关键特征。 这一视角可以解释动态自同构（DA）码在遭受缺失测量的噪声模型时逻辑信息的保护或测量。 我们使用受扰动测量序列的DA颜色码来演示这一点。 竞争自同构的框架捕捉了Floquet码的本质特征以及对噪声的鲁棒性，并可能阐明涉及拓扑序、自同构和容错的关键机制。