Photon T is used as a control qubit, and the photons A, 2, and B are used as target qubits in the CU operations. These CU operations are implemented by the CU gates, in which the C-path and G-path gates are consecutively performed by XKNLs, the qubus beams, the QND (PNR) measurements, and feed-forwards, as described in Section 2. If the unitary operator U in the middle between the C-path and G-path gates is σ_X the CU gate will become a CNOT, whereas if the operator is σ_Z the CU gate will become a CZ. For the BTQI scheme, the details of this CU gate are presented in Appendix A.