Steane code single qubit Clifford gates

Abstract

We apply single ‘logical’ qubit Clifford gates to states encoded in the [7,1,3] quantum error correction code in a nonequiprobable Pauli matrix error environment. The gates we analyze are the NOT, Phase, and Hadamard gates. We calculate accuracy measures of the applied gates by determining output state and logical gate fidelities. The latter is determined from the logical gate -matrix. In addition, we apply perfect and noisy quantum error correction to the output state of the Clifford gate. Perfect error correction allows the determination of whether errors that occurred during the gate are ‘correctable’. Noisy error correction gives an idea of what can be expected in a realistic quantum computation.