用不可约表面码设计逻辑门

中文摘要 AI 辅助

容错量子计算通常依赖于一组固定的逻辑原语，而实现其他所需操作可能需要大量资源。我们引入了不可约表面码（ISCs），这是一种二维拓扑量子纠错码，被设计用于横向实现一组预定的逻辑门。这些设计的门只需满足两个条件：（i）它们生成一个有限群，该群在全局相位上由Eastin-Knill定理强制决定；（ii）它们是不可约的，即任何与这组门交换的算子都必须与恒等算子成比例。这可以容纳任意有限的对角门群和任意的可逆经典门，因为每个都可以嵌入到更大的不可约有限门群中。它还使得逻辑门能够超越Clifford层级的每个有限层级。为了将这些操作整合到表面码计算中，我们进一步开发了晶格手术协议，以在表面码和满足两个充分条件之一的ISCs之间传输编码信息。这些结果共同建立了一种系统方法，用于定制拓扑码以适应所需的逻辑操作，并将其集成到常规计算中。

英文摘要

Fault-tolerant quantum computation typically relies on a fixed set of logical primitives, while realizing other desired operations can require substantial resources. We introduce irrep surface codes (ISCs), two-dimensional topological quantum error-correcting codes engineered to transversally implement a prescribed set of logical gates. The engineered gates only need to satisfy two conditions: (i) they generate a finite group, which, up to global phases, is forced by the Eastin-Knill theorem, and (ii) they are irreducible, meaning that any operator commuting with the set of gates must be proportional to the identity. This accommodates arbitrary finite groups of diagonal gates and arbitrary reversible classical gates, since each can be embedded into a larger irreducible finite group of gates. It also enables logical gates outside every finite level of the Clifford hierarchy. To incorporate these operations into surface-code computations, we further develop lattice-surgery protocols to transfer the encoded information between surface codes and ISCs obeying either of two sufficient conditions. Together, these results establish a systematic method for tailoring topological codes to desired logical operations and integrating them into conventional computations.

发表机构

• Purdue University（普渡大学）
• New York University（纽约大学）
• State University of New York at Stony Brook（纽约州立大学石溪分校）
• Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
• Southern Denmark University（南丹麦大学）

机构由 AI 辅助整理，请以论文原文为准。

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28+32 pages, 5+6 figures