Practical quantum error correction with the XZZX code and Kerr-cat qubits

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 $gtrsim 64mu$s, and thermal photon population $lesssim 8%$. Such parameters are routinely achieved in superconducting circuits.