Extend the Near-Term Magic-State Factory via Efficient C_xyz Cultivation

Magic states, including T-state and C_xyz-state for incommensurate π/4 and π/6 single-qubit rotations, provide crucial non-Clifford resources for fault-tolerant universal quantum computing. High-fidelity production of various magic states supports a large magic-state factory, substantially reducing the overall algorithmic overhead. While recent magic-state cultivation efficiently prepares high-fidelity T-states, the C_xyz-state cultivation remains absent. We address this problem by providing an equally efficient cultivation protocol in the surface code. We introduce a qutrit-assisted cultivation scheme, overcoming the key obstruction in applying the standard "state stabilizer check" in preparing the C_xyz-state. We then develop an adaptive teleportation protocol to mitigate the overhead associated with the indeterminacy in injecting the corresponding non-Clifford gate. To benchmark the protocol, we devise an iterative error simulator between qutrit and qubit Clifford circuits using error twirling, efficiently simulating hybrid qubit-qutrit systems. Our protocol achieves comparable logical error rates, post-selection rates, and space-time cost with the T-state cultivation. Together, this work paves the way for a low-overhead and diversified magic-state factory for near-term robust universal quantum computing.