Single-qudit universality for Clifford gate sets plus one non-Clifford gate follows a trichotomy determined by the prime factorization of the local dimension d.
Forp≥3, this order is strictly smaller than that of the sym- metric group|S p2 |= (p 2)!
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Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources
Single-qudit universality for Clifford gate sets plus one non-Clifford gate follows a trichotomy determined by the prime factorization of the local dimension d.