Fukui Kosuke, Tomita Akihisa, Okamoto Atsushi
Graduate School of Information Science and Technology, Hokkaido University Kita14-Nishi9, Kita-ku, Sapporo 060-0814, Japan.
Phys Rev Lett. 2017 Nov 3;119(18):180507. doi: 10.1103/PhysRevLett.119.180507.
To implement fault-tolerant quantum computation with continuous variables, Gottesman-Kitaev-Preskill (GKP) qubits have been recognized as an important technological element. However, the analog outcome of GKP qubits, which includes beneficial information to improve the error tolerance, has been wasted, because the GKP qubits have been treated as only discrete variables. In this Letter, we propose a hybrid quantum error correction approach that combines digital information with the analog information of the GKP qubits using a maximum-likelihood method. As an example, we demonstrate that the three-qubit bit-flip code can correct double errors, whereas the conventional method based on majority voting on the binary measurement outcome can correct only a single error. As another example, we show that a concatenated code known as Knill's C_{4}/C_{6} code can achieve the hashing bound for the quantum capacity of the Gaussian quantum channel (GQC). To the best of our knowledge, this approach is the first attempt to draw both digital and analog information to improve quantum error correction performance and achieve the hashing bound for the quantum capacity of the GQC.
为了实现连续变量的容错量子计算，戈特斯曼 - 基塔耶夫 - 普雷斯基尔（GKP）量子比特已被视为一种重要的技术元素。然而，GKP量子比特的模拟结果，其中包含有助于提高容错能力的有益信息，却一直被浪费，因为GKP量子比特一直仅被视为离散变量。在本信函中，我们提出一种混合量子纠错方法，该方法使用最大似然法将数字信息与GKP量子比特的模拟信息相结合。例如，我们证明三量子比特位翻转码可以纠正双错误，而基于对二进制测量结果进行多数表决的传统方法只能纠正单个错误。再如，我们表明一种被称为基尔的C₄/C₆码的级联码可以达到高斯量子信道（GQC）量子容量的哈希界。据我们所知，这种方法是首次尝试利用数字和模拟信息来提高量子纠错性能并达到GQC量子容量的哈希界。
