标题： 用于二项式码的振幅混合误差透明门的数学结构 显示英文标题

标题： A Mathematical Structure for Amplitude-Mixing Error-Transparent Gates for Binomial Codes

摘要： 量子信息的玻色编码相对于量子比特寄存器编码，提供了硬件高效且具有噪声偏好的量子错误校正方法。 实现主要集中在存储的空闲量子信息的错误校正上，而量子算法可能需要高占空比的主动控制。 误差透明操作是一种在操作过程中保持误差率的方法，但据我们所知，迄今为止，只有相位门对于二项式编码被明确地给出了误差透明的表述。 在此，我们引入了“奇偶嵌套”操作的概念，并展示了如何设计这些操作，以实现对二项式编码的连续振幅混合逻辑门，这些逻辑门对光子丢失信道完全误差透明。 对于一个可以抵御 l 次光子丢失的二项式编码，该结构需要$\lfloor$l/2$\rfloor$ + 1 阶广义压缩在奇偶嵌套操作中，以完全保留这种保护。 我们进一步表明，仅需一阶压缩即可实现对所有可校正的光子跳跃的误差透明，但不包括无跳跃错误。 最后，我们评论了实现这一概念的可能实验方法。 显示英文摘要

摘要： Bosonic encodings of quantum information offer hardware-efficient, noise-biased approaches to quantum error correction relative to qubit register encodings. Implementations have focused in particular on error correction of stored, idle quantum information, whereas quantum algorithms are likely to desire high duty cycles of active control. Error-transparent operations are one way to preserve error rates during operations, but, to the best of our knowledge, only phase gates have so far been given an explicitly error-transparent formulation for binomial encodings. Here, we introduce the concept of 'parity nested' operations, and show how these operations can be designed to achieve continuous amplitude-mixing logical gates for binomial encodings that are fully error-transparent to the photon loss channel. For a binomial encoding that protects against l photon losses, the construction requires $\lfloor$l/2$\rfloor$ + 1 orders of generalized squeezing in the parity nested operation to fully preserve this protection. We further show that error-transparency to all the correctable photon jumps, but not the no-jump errors, can be achieved with just a single order of squeezing. Finally, we comment on possible approaches to experimental realization of this concept.