Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a topological circuit, for which braided circuits represent one candidate model. Given the large overhead associated with encoded circuits, it is paramount to reduce their size in terms of computation time and qubit number through circuit compression. While these optimizations have typically been performed in the language of three-dimensional diagrams, such a representation does not allow an efficient, general, and scalable approach to reduction or verification. We propose the use of the ZX-calculus as an intermediate language for braided circuit compression, demonstrating advantage by comparing results using this approach with those previously obtained for the compression of $|A⟩$ and $|Y⟩$ state distillation circuits. We then provide a benchmark of our method against a small set of $\text{Clifford}+T$ circuits, yielding compression percentages of $\sim 77\%$. Our results suggest that the overheads of braided, defect-based circuits are comparable to those of their lattice-surgery counterparts, restoring the potential of this model for surface-code quantum computation.

中文翻译：

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ZX演算辅助的量子编织电路的有效压缩

将量子算法映射到任何实际的大型量子计算机将需要一系列的编译和优化。在容错编码级别，此过程的一个可能要求是转换为拓扑电路，其中编织电路代表一个候选模型。考虑到与编码电路相关的大量开销，通过电路压缩来减小它们在计算时间和量子位数量方面的大小至关重要。尽管这些优化通常是用三维图的语言执行的，但这种表示方式不允许采用有效，通用和可扩展的方法来进行缩减或验证。我们建议使用ZX微积分作为编织电路压缩的中间语言，$|\mathrm{一种}⟩$ 和 $|ÿ⟩$状态蒸馏回路。然后，我们针对少量的方法提供了我们方法的基准$\text{克利福德}+Ť$ 回路，产生的压缩百分比为 $〜77％$。我们的结果表明，基于缺陷的编织电路的开销与其晶格手术对应的开销相当，从而恢复了该模型在表面编码量子计算中的潜力。