  The development of robust architectures capable of large-scale fault-tolerant
quantum computation should consider both their quantum error-correcting codes,
and the underlying physical qubits upon which they are built, in tandem.
Following this design principle we demonstrate remarkable error correction
performance by concatenating the XZZX surface code with Kerr-cat qubits. We
contrast several variants of fault-tolerant systems undergoing different
circuit noise models that reflect the physics of Kerr-cat qubits. Our
simulations show that our system is scalable below a threshold gate infidelity
of $p_\mathrm{CX} \sim 6.5\%$ within a physically reasonable parameter regime,
where $p_\mathrm{CX}$ is the infidelity of the noisiest gate of our system; the
controlled-not gate. This threshold can be reached in a superconducting circuit
architecture with a Kerr-nonlinearity of $10$MHz, a $\sim 6.25$ photon cat
qubit, single-photon lifetime of $\gtrsim 64\mu$s, and thermal photon
population $\lesssim 8\%$. Such parameters are routinely achieved in
superconducting circuits.
