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_{CX}∼6.5% within a physically reasonable parameter regime, where p_{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 10MHz, an approximately 6.25-photon cat qubit, single-photon lifetime of ≳64μs, and a thermal photon population ≲8%. Such parameters are routinely achieved in superconducting circuits.