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Glossary

Quantum glossary

Clifford gates

Also: Clifford group, Gottesman–Knill theorem, Clifford circuit

The gates — generated by H, S and CNOT — that turn every Pauli operator into another Pauli operator.

Because they only shuffle Paulis, a circuit of Clifford gates can be simulated efficiently on a classical computer however many qubits and however much entanglement it has (the Gottesman–Knill theorem). So entanglement alone is not what makes quantum computing hard to simulate: it takes a non-Clifford gate such as T.

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Related terms

  • Stabilizer formalism — A way to describe a quantum state by the Pauli operators that leave it unchanged, instead of by its amplitudes.
  • Universal gate set — A small set of gates from which any quantum computation can be approximated to arbitrary accuracy.
  • Pauli gates (X, Y, Z) — The three basic single-qubit operations: X flips the bit, Z flips the phase, Y does both.
  • Hadamard gate — The single-qubit gate that turns |0⟩ into an equal superposition of |0⟩ and |1⟩, and back again.