Figure 3

Two-photon four-qubit Fredkin gate acting on the polarization and spatial DoFs.
Hadamard transformation HP can be achieved by employing a half-wave plate oriented at 22.5°. Phase shifter Pπ completes the operations |R〉 → −|R〉 and |L〉 → −|L〉. The local classical feed-forward single-qubit operations are not shown in the sketch.