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

Abstract

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