Cross-Resonant Gates in Hybrid Fluxonium-Transmon Systems

We propose a scalable fluxonium-transmon-fluxonium (FTF) system that utilizes a central transmon to mediate high-fidelity gates and parity checks between two fluxonium qubits without the need for strong non-local interactions. This approach suppresses unwanted long-range interactions, which is critical for developing larger quantum processors. First, we analyze the performance of cross-resonance (CR) CNOT gates between a fluxonium and a transmon. We show that even in the presence of a spectator qubit, these gates maintain high fidelity with coherent errors on the order of $10^{-5}$. We then demonstrate that these gates, when applied sequentially, enable high-fidelity parity checks and logical fluxonium-fluxonium CNOT gates. In addition, the central transmon can facilitate the readout of the neighboring fluxoniums, consolidating multiple critical functions into a single ancilla. Our work establishes the viability of a dual-species architecture as a promising path toward fault-tolerant quantum computation.