Cavity-QED tools for MBQC with optical binomial-codes

Abstract: Measurement-based quantum computation (MBQC) offers a promising paradigm for photonic quantum computing, but its implementation requires the generation of specific non-Gaussian resource states. While continuous-variable encodings such as the highly complex (GKP) states have been widely studied, the much simpler binomial codes offer an experimentally accessible alternative, though they demand a distinct set of operational tools. Here, we present a toolkit for MBQC using optical binomial codes, detailing a cavity-QED protocol for conditional generation of cluster states and the implementation of Pauli measurements. Our work proposes the first steps for existing optical atom-cavity architectures to lay the groundwork for their use in quantum computation.