Practical Quantum Error Correction with the XZZX Code and Kerr-Cat Qubits
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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 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 (cid:2) 64 μ s, and a thermal photon population (cid:3) 8%. Such parameters are routinely achieved in superconducting circuits. DOI: