Figure 1

Key parameters of the system. The gate between the qubits is created by an interaction between the vertical polarization modes inside the device. The modes interact with a strength $ϵ$, for a time $t$. While passing through the medium the modes undergo one- and two-photon loss with the rates ${\gamma }_1$ and ${\gamma }_2$, respectively. The whole gate forms a dual-rail CSIGN gate for polarization encoded qubits while the region inside the dashed box forms a single-rail encoded CSIGN gate.Reuse & Permissions

Figure 2

Process fidelity of the gate with the ideal gate $\mathbb{S}$, for (a) $\gamma =20$, (b) $\gamma =100$, and (c) $\gamma =500$. The dashed lines represent the 19 beamsplitter case.Reuse & Permissions

Figure 3

(Color online) The scaling of the process fidelity with $\gamma$ for optimal $\tau ={\tau }_{\mathrm{opt}}$ (separate optimization for each point shown). For comparison the green (coarse dashed) and red (fine dashed) lines represent the 7 and 19 beamsplitter case, respectively, in the alternate model. (a) The unencoded gate, (b) the unbalanced encoded gate, and (c) the balanced encoded gate (which can attain fidelity 1 in the large $\tau$ limit).Reuse & Permissions

Figure 4

To perform an encoded CSIGN operation (i) a pair of qubits goes through the nonlinear CSIGN gate and the photons may be lost in the interaction. (ii) Detect these qubits in the ∣±⟩ $\left(X\right)$ basis. (iii-a) If measurements indicated that no photons were lost, measure the remaining parity qubit in the computational $(A=Z)$ basis. The CSIGN operation has been successfully performed. (iii-b) If measurements indicated loss, measure the remaining parity qubits in the ∣±⟩ $(A=X)$ basis to disentangle and attempt gate on the next redundantly encoded qubits. (iv) Depending on the measurement results phase corrections may need to be applied to remaining qubits. Note that the double line indicates classical information.Reuse & Permissions

Figure 5

(Color online) Average number of photons consumed per gate operation, $\overline{n}$, as a function of the probability of total failure $P_0$ for a target fidelity of $F_0=99.9\%$. (a) The LOQC parity gate. (b) The unbalanced Zeno gate with $\gamma =3600$ (minimum $\gamma$ that achieves the target fidelity). The failure probability can be reduced by increasing the code size without increasing $\overline{n}$, (c)–(f) show an additional 1–4 redundant qubits ($m=2–5)$. The balanced Zeno gate allows $\gamma$ to be traded off against $P_0$: (g)–(k) are for $\gamma =4000,2000,1000,500,250$, respectively, and four additional redundant qubits as in (f).Reuse & Permissions