Erasure Doubles: Designing erasure qudits for topological codes via dual rail-style encodings

The superconducting dual rail cavity qubit has seen an incredible surge in interest in the past few years. One key paradigm of operation is to use this as the base qubit in surface codes. In this talk, we discuss techniques to design dual rail-style qudits with erasure-preserving gates for non-abelian topological codes, using only components that have been experimentally realized. These encodings may be viewed as bosonic codes that generalize schemes concatenating dual-rail qubits and the surface code. As applications, we study ground state preparation of the S₃ quantum double model, as well as error correction of the D₄ quantum double model.