Fault-Tolerant Fusion-Based Quantum Computing with the 4-Legged Cat Code

With its ability to correct for single-photon loss, the 4-legged cat code stands out as a promising bosonic quantum memory, becoming the first code to surpass the QEC breakeven point [1]. We extend its capabilities with a universal set of operations composed of destructive Bell measurements and entangled resource state generation. These operations are efficiently implemented using standard cQED tools: inter-cavity beam-splitter coupling, cavity displacements, cavity-transmon dispersive coupling, and transmon drives. Notably, the Bell measurements are not limited by undesired non-linearities in the cavities, particularly cavity self-Kerr. Additionally, analytics and pulse-level simulations demonstrate that these operations are, at worst, second-order sensitive to both photon loss in the storage cavity and decoherence in the transmons. The proposed universal set of operations is particularly suited for fusion-based fault-tolerant quantum computation with the XZZX cluster state. The inherent first-order robustness promises a suppression of physical qubit error rates beyond what is expected from unencoded physical qubits.

[1] Ofek et. al. Nature 536, 441–445 (2016)