Magic state injection on IBM quantum processors above the distillation threshold

The surface code family is a promising approach to implementing fault-tolerant quantum computations. Universal fault-tolerance requires error-corrected non-Clifford operations, in addition to Clifford gates, and for the former, it is imperative to experimentally demonstrate additional resources known as magic states. Another challenge is to efficiently embed surface codes into quantum hardware with connectivity constraints. This work simultaneously addresses both challenges by employing a qubit-efficient rotated heavy-hexagonal surface code for IBM quantum processors (ibmfez) and implementing the magic state injection protocol. Our work reports error thresholds for both logical bit- and phase-flip errors, of Formula: see text and Formula: see text, respectively, which are higher than the threshold values previously reported with traditional embedding. The post-selection-based preparation of logical magic states Formula: see text and Formula: see text achieve fidelities of Formula: see text and Formula: see text, respectively, which are both above the magic state distillation threshold. The post-selection process yields an average success rate of Formula: see text. Additionally, we report the minimum fidelity among injected arbitrary single logical qubit states as Formula: see text. Our work demonstrates the potential for realising non-Clifford logical gates by producing high-fidelity logical magic states on IBM quantum devices.