We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat codes that can outperform previous constructions while requiring a similar type of overhead. Our polytope-based cat codes consist of sets of points with large separation that at the same time form averaging sets known as spherical designs. We also recast concatenations of CSS codes with cat codes as quantum spherical codes, revealing a new way to autonomously protect against dephasing noise.

翻译：我们提出了一种框架，用于构建定义在球面上的量子码，将这些码重新诠释为经典球面码的量子对应物。我们将此框架应用于玻色子编码，获得了猫码的多模扩展，这些扩展在类似开销条件下能够超越先前的构造。基于多面体的猫码由具有大间隔的点集构成，这些点集同时形成被称为球面设计的平均集。我们还将CSS码与猫码的级联重新解释为量子球面码，揭示了自主抵御退相位噪声的新途径。