Hu Dong-Long, Cai Weizhou, Zou Chang-Ling, Xiang Ze-Liang
School of Physics, Sun Yat-sen University, Guangzhou, 510275, China.
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.
Nat Commun. 2025 Aug 16;16(1):7647. doi: 10.1038/s41467-025-62898-1.
Bosonic systems offer unique advantages for quantum error correction, as a single bosonic mode provides a large Hilbert space to redundantly encode quantum information. However, previous studies have been limited to exploiting symmetries in the quadrature phase space. Here we introduce a unified framework for encoding a qubit utilizing the symmetries in the phase space of number and phase variables of a bosonic mode. The logical codewords form lattice structures in the number-phase space, resulting in rectangular, oblique, and diamond-shaped lattice codes. Notably, oblique and diamond codes exhibit a number-phase vortex effect, where number-shift errors induce discrete phase rotations as syndromes, enabling efficient correction via phase measurements. These codes show significant performance advantages over conventional quadrature codes against dephasing noise in the potential one-way quantum communication applications. Our generalized number-phase codes open up new possibilities for fault-tolerant quantum computation and extending the quantum communication range with bosonic systems.
玻色子系统为量子纠错提供了独特的优势，因为单个玻色子模式提供了一个大的希尔伯特空间来冗余地编码量子信息。然而，先前的研究仅限于利用正交相空间中的对称性。在这里，我们引入了一个统一的框架，用于利用玻色子模式的数和相位变量的相空间中的对称性来编码一个量子比特。逻辑码字在数相空间中形成晶格结构，从而产生矩形、斜交和菱形晶格码。值得注意的是，斜交码和菱形码表现出数相涡旋效应，其中数移误差会引起离散的相位旋转作为错码，从而能够通过相位测量进行有效校正。在潜在的单向量子通信应用中，这些码相对于传统的正交码在抗退相噪声方面表现出显著的性能优势。我们的广义数相码为容错量子计算以及扩展玻色子系统的量子通信范围开辟了新的可能性。
