Logical Magic State Preparation with Fidelity beyond the Distillation Threshold on a Superconducting Quantum Processor

Fault-tolerant quantum computing based on surface code has emerged as an attractive candidate for practical large-scale quantum computers to achieve robust noise resistance. To achieve universality, magic states preparation is a commonly approach for introducing non-Clifford gates. Here, we present a hardware-efficient and scalable protocol for arbitrary logical state preparation for the rotated surface code, and further experimentally implement it on the Zuchongzhi 2.1 superconducting quantum processor. An average of 0.8983 1 0.0002 logical fidelity at different logical states with distance three is achieved, taking into account both state preparation and measurement errors. In particular, the logical magic states IA pi/4)L, IH)L, and IT)L are prepared nondestructively with logical fidelities of 0.8771 1 0.0009, 0.9090 1 0.0009, and 0.8890 1 0.0010, respectively, which are higher than the state distillation protocol threshold, 0.859 (for H-type magic state) and 0.827 (for T-type magic state). Our work provides a viable and efficient avenue for generating high-fidelity raw logical magic states, which is essential for realizing non-Clifford logical gates in the surface code.