Benchmarking Single-Qubit Gates on a Noise-Biased Qubit: Kerr cat qubit

The exploration of noise structures in quantum systems has driven the development of hardware-efficient quantum error correction protocols. Specifically, developing quantum error correction codes tailored for biased-noise systems has emerged as a promising avenue to achieve fault-tolerance due to their high error thresholds. However, the operation of such protected platforms is believed to be challenging and their comprehensive gate benchmarking and noise characterization remain incomplete, hindering their application in quantum error correction. In this work, we leverage Schrödinger cat states in a 2D superconducting nonlinear oscillator and novel benchmarking tools to thoroughly characterize and demonstrate the high-fidelity quantum operations with performance crossing the fault-tolerant threshold of the XZZX surface code. This result thus embodies a transformative milestone in the exploration of quantum architectures protected from an error channel. Notably, our framework is extensible to other types of biased-noise systems, paving the way for systematic characterization and validation of novel quantum platforms with structured noise.