Extended Data Fig. 5: FT logical T gate circuits.
(a) The \({T}_{L}^{Z}\) gate on the [[10, 1, 2]] code can be implemented by applying single-qubit T and T† gates to qubits 1 - 7 and a CCZ gate to qubits 8, 9, and 10. An additional minimal error-detection block has to be performed before applying this gate that checks only for potentially dangerous propagated X errors occurring during the initialization of the logical \({\left\vert +\right\rangle }_{L}\). (b) The \({T}_{L}^{X}={H}^{\otimes 10}{T}_{L}^{Z}{H}^{\otimes 10}\) on the rotated [[10, 1, 2]] code is implemented analogously by applying single-qubit TX and \({T}_{X}^{\dagger }\) gates on qubits 1 -7 and a CCX gates to qubits 8, 9, and 10.
