Table 1 Characteristic of single CZ gate on metasurface
(a) Encoding rules of polarization qubits | ||||||
|---|---|---|---|---|---|---|
| Â | Control | Target | Auxiliary | |||
Polarization state | \({| R\left.\right\rangle }_{0}\) | \({| L\left.\right\rangle }_{0}\) | \({| R\left.\right\rangle }_{+1}\) | \({| L\left.\right\rangle }_{+1}\) | \({| R\left.\right\rangle }_{+2}\) | \({| L\left.\right\rangle }_{-1}\) |
Encoded qubit state | \({| 0\left.\right\rangle }_{C}\) | \({| 1\left.\right\rangle }_{C}\) | \({| 1\left.\right\rangle }_{T}\) | \({| 0\left.\right\rangle }_{T}\) | None | None |
Mode label | \({\hat{C}}_{0}^{R}\) | \({\hat{C}}_{1}^{L}\) | \({\hat{T}}_{1}^{R}\) | \({\hat{T}}_{0}^{L}\) | \({\hat{V}}^{R}\) | \({\hat{V}}^{L}\) |
(b) Truth table of 2-qubit input states | ||
|---|---|---|
Input | Output | Post-selection probability |
\({| 0\left.\right\rangle }_{C}{| 0\left.\right\rangle }_{T}\) | \({| 0\left.\right\rangle }_{C}{| 0\left.\right\rangle }_{T}\) | 1/9 |
\({| 0\left.\right\rangle }_{C}{| 1\left.\right\rangle }_{T}\) | \({| 0\left.\right\rangle }_{C}{| 1\left.\right\rangle }_{T}\) | 1/9 |
\({| 1\left.\right\rangle }_{C}{| 0\left.\right\rangle }_{T}\) | \({| 1\left.\right\rangle }_{C}{| 0\left.\right\rangle }_{T}\) | 1/9 |
\({| 1\left.\right\rangle }_{C}{| 1\left.\right\rangle }_{T}\) | \(-{| 1\left.\right\rangle }_{C}{| 1\left.\right\rangle }_{T}\) | 1/9 |
