Magic State Distillation with Reduced Time Cost

We have noted that performing non-Clifford <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T$</tex> operations in a fault-tolerant quantum computing system requires magic states. The magic state distillation (MSD) process, which generates high-fidelity magic states, incurs significant time and space costs. We propose a method for implementing an MSD with a low time cost for the system where a surface code is applied. The proposed method utilizes a deterministic correction operator and leverages 4-qubit twist defects. Therefore, the time cost is reduced to three times the code distance, much lower than in previous works. Reducing computation time benefits the overall speed of the computing system, which in turn provides a foundation for realizing quantum computational advantages.