Clifford circuit

A Clifford circuit is composed entirely of Clifford gates. It maps Pauli operators to Pauli operators in the Heisenberg picture and stabilizer states to stabilizer states in the Schrödinger picture.

Table of contents
- Gottesman--Knill theorem Clifford circuit
  - Extended Gottesman--Knill theorem Gottesman--Knill theorem
- Clifford frame Clifford circuit

Gottesman--Knill theorem

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The Gottesman--Knill theorem gives a classical polynomial-time simulation of quantum computations built from stabilizer-state preparation, Clifford gates, and adaptive measurements of Pauli observables.

Extended Gottesman--Knill theorem

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The extended Gottesman--Knill theorem allows arbitrary product-state inputs to a unitary Clifford circuit. Computational-basis output is weakly simulable for any number of measured qubits and strongly simulable for logarithmically many measured qubits.

A Clifford frame records a known Clifford transformation classically instead of applying it physically. Updating the frame changes the Pauli observables used for later measurements while preserving the represented quantum computation.