Figure 1

Schematic of the heralded linear optical Fredkin gate comprising four heralded CNOT gates. Lowercase letters and numbers label the beams. The input control qubit is in beam $c_{\text{in}}$ and the two input target qubits are in beams $t_{1\text{in}}$ and $t_{2\text{in}}$. Polarizing beam splitters (PBS) transmit horizontally polarized photons and reflect vertically polarized photons. Half-wave plates HWP1 and HWP3 are oriented at 67.5°. HWP2 and HWP4 are set to 22.5°. The gate succeeds if the two photon number resolving detectors D1 and D2 detect no photons. The output control and target states lie in modes $c$, $t_1$, and $t_2$.Reuse & Permissions

Figure 2

Schematic of the post-selected linear optical Fredkin gate using two controlled-NOT (CNOT) gates. Lowercase letters and numbers label the beams. The control and two target qubits are input in beams $c_{\text{in}}$, $t_{1\text{in}}$, and $t_{2\text{in}}$. Polarizing beam splitters (PBSs) transmit horizontally polarized photons and reflect vertically polarized photons. Half-wave plates HWP1, HWP3, and HWP5 are oriented at 67.5°. HWP2, HWP4, and HWP6 are set to 22.5°. This gate succeeds conditioned on exactly one photon in each of the output beams $c$, $t_1$, and $t_2$. Symbols “$\times$” denote the discarded outputs.Reuse & Permissions

Figure 3

Optical realization of a post-selected Fredkin gate. Lowercase letters and numbers label the beams. Photons in beams $c_{\text{in}}$, $t_{1\text{in}}$, and $t_{2\text{in}}$ are the control and two target qubits. Polarizing beam splitters (PBSs) transmit horizontally polarized $\left(|H⟩\right)$ photons and reflect vertically polarized $\left(|V⟩\right)$ photons. A heralded controlled-NOT (CNOT) gate proposed in Ref. [7] lies in the dotted box. EPR is an ancillary Bell state source. RPBS, transmitting 45° polarized $\left(|+⟩\right)$ photons and reflecting $-45°$ polarized $\left(|V⟩\right)$ photons, can be realized by inserting one half-wave plate (HWP) oriented at 22.5° in each of the two inputs and two outputs of a PBS. D1 and D2 are photon detectors detecting $+/-$ basis and $H/V$ basis, respectively. A post-selected CNOT gate suggested in Ref. [12] is enclosed by the dashed box. Beam splitters are represented as black lines with their reflectivity indicated aside and dotted line indicates the surface from which a sign change occurs upon reflection. HWP1, HWP3, and HWP5 are oriented at 67.5°. HWP2, HWP4, and HWP6 are set to 22.5°. HWP7 is set to 45°. This gate succeeds conditioned on the coincidence of the successful detection at D1 and D2 and exactly one photon in each of the output beams $c$, $t_1$, and $t_2$. Symbols “$\times$” denote the discarded outputs.Reuse & Permissions

Figure 4

Schematic of the controlled-NOT (CNOT) gate demonstrated in Ref. [17]. Lowercase letters label the beams. Polarizing beam splitters (PBS) transmit horizontally polarized photons and reflect vertically polarized photons. The control (target) photon is input in mode $c_{\text{in}}$ $\left(t_{\text{in}}\right)$ and output is in mode $c_{\text{out}}$ $\left(t_{\text{out}}\right)$. BS1 and BS2 are both balanced beam splitters. HWP is a half-wave plate set to 45°.Reuse & Permissions

Figure 5

Optical realization of a post-selected linear optical Fredkin gate assisted by time entanglement. Lowercase letters and numbers label the beams. Photons in beams $c_{\text{in}}$, $t_{1\text{in}}$, and $t_{2\text{in}}$ are the control and two target qubits. Polarizing beam splitters (PBS) transmit horizontally polarized photons and reflect vertically polarized photons. BS is balanced beam splitter. Half-wave plates HWP1 and HWP3 are oriented at 67.5°. HWP2 and HWP4 are set to 22.5°. HWP5, HWP6, HWP7, and HWP8 are set to 45°. The gate succeeds in the case of threefold coincidence detection in the output modes $c$, $t_1$, and $t_2$. Symbols “$\times$” denote the discarded outputs.Reuse & Permissions