Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum computation. This universality is highly desired and often achieved using additional techniques such as code concatenation, code switching, or magic state distillation, which can be costly and only work for specific codes. This work implements logical Clifford and T gates through novel ancilla-mediated protocols to construct a universal fault-tolerant quantum gate set. Unlike traditional techniques, our implementation is deterministic, does not consume ancilla registers, does not modify the underlying data codes or registers, and is generic over all stabilizer codes. Thus, any single code becomes capable of universal quantum computation by leveraging helper codes in ancilla registers and mid-circuit measurements. Furthermore, since these logical gates are stabilizer code-generic, these implementations enable communication between heterogeneous stabilizer codes. These features collectively open the door to countless possibilities for existing and undiscovered codes as well as their scalable, heterogeneous coexistence.

翻译：容错量子计算使得量子计算能够在抵抗非期望噪声的同时得以执行。为实现这一目标，已发展出多种纠错码，但单独使用任何一种均无法实现通用量子计算。这种通用性备受期待，通常需借助额外技术实现，例如码级联、码切换或魔术态蒸馏，但这些方法可能代价高昂且仅适用于特定编码。本研究通过新颖的辅助比特介导协议实现了逻辑克利福德门与T门，从而构建了通用的容错量子门集合。与传统技术不同，我们的实现具有确定性，不消耗辅助寄存器，不修改底层数据码或寄存器，并且适用于所有稳定子码。因此，通过利用辅助寄存器中的辅助码和电路中间测量，任何单一编码均可实现通用量子计算。此外，由于这些逻辑门具有稳定子码通用性，该实现能够实现异构稳定子码间的通信。这些特性共同为现有及尚未发现的编码体系，以及它们可扩展的异构共存模式，开启了无限可能。