Magic state distillation (MSD) is a cornerstone of fault-tolerant quantum computing, enabling non-Clifford gates via state injection into stabilizer circuits. However, the substantial overhead of current MSD protocols remains a major obstacle to scalable implementations. We propose a general framework for pre-distillation, based on composite pulse sequences that suppress systematic errors in the generation of magic states. Unlike typical composite designs that target simple gates such as X, Z, or Hadamard, our schemes directly implement the non-Clifford T gate with enhanced robustness. We develop composite sequences tailored to the dominant control imperfections in superconducting, trapped-ion, neutral-atom, and integrated photonic platforms. To quantify improvement in the implementation, we introduce an operationally motivated fidelity measure specifically tailored to the T gate: the T-magic error, which captures the gate's effectiveness in preparing high-fidelity magic states. We further show that the error in the channel arising from the injection of faulty magic states scales linearly with the leading-order error of the states. Across all platforms, our approach yields high-fidelity T gates with reduced noise, lowering the number of distillation levels by up to three. This translates to exponential savings in qubit overhead and offers a practical path toward more resource-efficient universal quantum computation.
Erew et al. (Wed,) studied this question.