Quantum glossary
Universal gate set
Also: clifford+t, native gates
A small set of gates from which any quantum computation can be approximated to arbitrary accuracy.
A common choice is {H, S, T, CNOT}. Clifford gates alone (H, S, CNOT) can be simulated efficiently on a classical computer; adding the T gate is what makes the set universal — and what makes fault-tolerant computation expensive.