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

TL;DR

This paper demonstrates that concatenating the XZZX surface code with Kerr-cat qubits enables scalable quantum error correction with high thresholds, suitable for superconducting circuit implementations.

Contribution

It introduces a fault-tolerant quantum error correction scheme combining the XZZX code with Kerr-cat qubits, showing scalability and practical thresholds in superconducting circuits.

Findings

Error correction threshold of ~6.5% gate infidelity.

Scalability demonstrated with realistic superconducting parameters.

Compatible with current superconducting circuit technology.

Abstract

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.