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The Generalized Semi-Clifford Conjecture Holds at Level 4
The Clifford hierarchy $\mathsf{C}_1 \subset \mathsf{C}_2 \subset \cdots$ was introduced by Gottesman and Chuang (arXiv:quant-ph/9908010) to characterize gates that admit fault-tolerant implementation by gate teleportation. Yet, despite its rich mathematical structure and the attention it has receiv
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