Researchers have analyzed the effectiveness of photon catalysis for generating squeezed coherent state superpositions (squeezed cat states), which are crucial for quantum computing and error correction in bosonic platforms. These non-Gaussian quantum states are experimentally challenging to produce, often requiring probabilistic protocols. The study employed the stellar rank formalism to characterize the non-Gaussian complexity of input resources and generated states, enabling a systematic comparison of the achieved fidelity with the theoretically maximum achievable fidelity.

The analysis identified parameter regimes where the considered catalysis protocols are optimal, achieving high-fidelity approximations of target states with minimal resources. Furthermore, the performance of photon catalysis was benchmarked against Gaussian boson sampling-inspired protocols, highlighting the advantages of deterministic Fock state sources. The generation of other non-Gaussian resources relevant for quantum error correction, such as squeezed Fock states, was also investigated.

To account for experimental imperfections, the study modeled losses across all optical modes using a Hilbert space truncation approach in the Fock basis, analyzing the robustness of the generated states under realistic conditions. The results quantify the trade-offs between non-Gaussian resource complexity, achievable fidelity, and losses in photon catalysis protocols, providing practical guidelines for near-term photonic implementations.