Quantum Spherical Codes II

Quantum spherical codes (QSCs) [Nature Physics volume 20, pages 1300–1305 (2024)] provide a general framework to encode quantum information into multiple bosonic modes using superpositions of coherent states. Building on that work, we come up with new ways to construct QSCs from classical codes. We devise methods to obtain logical gates at high levels of the Clifford hierarchy using as few as one mode encodings. We give a recipe to implement a universal set of gates. Using algebraic tools such as Groebner bases, we reduce the original degree of the stabilizing dissipators of several codes, improving their practical feasibility.