Quantum communication technologies will play an important role in quantum information processing in the near future as we network devices together. However, their implementation is still a challenging task due to both loss and gate errors. Quantum error correction codes are one important technique to address this issue. In particular, the Quantum Reed-Solomon codes are known to be quite efficient for quantum communication tasks. The high degree of physical resources required, however, makes such a code difficult to use in practice. A recent technique called quantum multiplexing has been shown to reduce resources by using multiple degrees of freedom of a photon. In this work, we propose a method to decompose multi-controlled gates using fewer $\rm{CX}$ gates via this quantum multiplexing technique. We show that our method can significantly reduce the required number of $\rm{CX}$ gates needed in the encoding circuits for the quantum Reed-Solomon code. Our approach is also applicable to many other quantum error correction codes and quantum algorithms, including Grovers and quantum walks.
翻译:量子通信技术将在最近的将来随着我们的网络设备一起,在量子信息处理中发挥重要作用。 但是,由于损失和门错误,它们的实施仍是一项艰巨的任务。 量子错误校正代码是解决这一问题的重要技术之一。 特别是, 量子Reed- Solomon 代码对于量子通信任务来说相当有效。 但是,由于所需的大量物质资源,这种代码难以在实践中使用。 最近的一种称为量子多重x化的技术已经显示,通过光子自由的多重度来减少资源。 在这项工作中,我们提出了一个方法,通过量子多重x化技术将多控门用更少的 $\ rm{C{X} 来拆解。 我们表明,我们的方法可以大大减少量子Reed- Solomon 代码编码电路中所需的 $rm{C} 门数。 我们的方法也适用于许多其他量子错误校正代码和量子算法, 包括格罗弗斯和量步。