Kerr-cat Qubit Operations Below the Fault-tolerant Threshold

The ubiquitous noise in quantum system hinders the advancement of quantum information processing and has driven the emergence of different quantum error correction protocols. Among them, quantum error correction codes tailored for noise-biased qubits exhibit comparatively high error thresholds, making them a promising platform to achieve fault-tolerance. Nevertheless, their quantum operations are challenging and the demonstration of their performance beyond the fault-tolerant threshold remains incomplete. Here, we leverage Schrödinger cat states in scalable planar superconducting circuits to thoroughly characterize the high-fidelity single-qubit quantum operations on noise-biased qubits with systematic quantum tomography and benchmarking tools, demonstrating their state-of-the-art performance beyond the fault-tolerant threshold of the surface code. These results thus embody a transformative milestone in the exploration of quantum systems with structured noises. Notably, our framework is extensible to other structured-noise systems, paving the way for systematic characterization and validation of novel quantum platforms with structured noise.