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Glossary

Quantum glossary

Stabilizer formalism

Also: stabilizer state, stabilizer code, stabilizer group

A way to describe a quantum state by the Pauli operators that leave it unchanged, instead of by its amplitudes.

An n-qubit stabilizer state is pinned down by n commuting Pauli operators — n short strings rather than 2ⁿ numbers. It is not a simplification for beginners: nearly every quantum error-correcting code is defined this way, with fewer than n stabilizers so that a protected space is left over.

S|ψ⟩ = |ψ⟩ for every S in the stabilizer group; Bell pair: ⟨XX, ZZ⟩

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Related terms

  • Clifford gates — The gates — generated by H, S and CNOT — that turn every Pauli operator into another Pauli operator.
  • Pauli gates (X, Y, Z) — The three basic single-qubit operations: X flips the bit, Z flips the phase, Y does both.
  • Syndrome — The pattern of parity-check results that tells an error-correcting code where an error probably happened.
  • Code distance — The smallest number of qubits an error must touch to change the encoded information without being detected.