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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±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 |A^π/4⟩₋, |H⟩₋, and |T⟩₋ are prepared nondestructively with logical fidelities of 0. 8771±0. 0009, 0. 9090±0. 0009, and 0. 8890±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.
Ye et al. (Tue,) studied this question.