Figure 1

(Color online) Schematic setup for controlled-path gate. A PBS used in the circuit transmits the mode $|H⟩$ and reflects the mode $|V⟩$ of a single photon. Two qubus beams are coupled to the photonic modes as indicated. The XPM phases on the qubus beams $\theta$ and two phase shifters $-\theta$ are applied to the qubus beams. The QND module in dash-dotted line is used to perform number-resolving detection.Reuse & Permissions

Figure 2

(Color online) Schematic setup for merging gate. The ancilla photon in the state $|\pm ⟩$. The single-photon modes on paths 2 and 3 interact with the qubus beams in the pattern indicated in entangler. On the first (second) qubus beam, we use one XPM rotation $\theta$ to represent the coupling to the $|V⟩\left(|H⟩\right)$ mode on both paths 2 and 3. A BS and four ${\text{PBS}}_{\pm }$ divide the modes of the second photon to four paths, on which the QND modules in Fig. 1 are to detect the photon. The operations ${\sigma }_z$ are performed according to the feed-forwarded of the QNDs.Reuse & Permissions

Figure 3

(Color online) Schematic setup for the Fredkin gate. Two C-path and merging gates, together with the exchange of two path modes, are used to realize a Fredkin gate directly.Reuse & Permissions

Figure 4

(Color online) Schematic setup for Toffoli gate. The H mode of photon $C_1$ and the modes on path 3 after the first C-path gate control the target photon in the second C-path gate. A bit flip is performed on the target mode on path 5. The couplings of the qubus beams with the relevant photonic modes in C-path 2 are illustrated in dashed line. On the second qubus beam of the C-path 2 gate, we use one XPM rotation $\theta$ to represent the couplings to both $|H⟩$ modes of paths 1 and 3.Reuse & Permissions

Figure 5

(Color online) Schematic setup for a triple-control Toffoli gate, with the $|V⟩$ modes of three photons from $C_1$ to $C_3$ controlling the bit flip ${\sigma }_x$ on the target photon $T$. As a simple generalization of the design in Fig. 4, it applies another modified C-path gate—C-path 3—illustrated in dashed line. On the second qubus beam of the C-path 3 gate, we use just one XPM rotation $\theta$ to represent the couplings to the $|H⟩$ mode of paths 1, 3, and 5, respectively. Only one ancilla photon will be necessary for the three merging gates if we apply the detections with QND modules.Reuse & Permissions