Table 1 Currently available qumode operations as gates
From: Photonic counterdiabatic quantum optimization algorithm
Gate | Expression | Type |
|---|---|---|
Rotation or Phase-shift | \(R(\phi )=\exp [i\phi \hat{n}]\) | Gaussian |
Displacement | \(D(\alpha )=\exp [\alpha \hat{a}-{\alpha }^{* }{\hat{a}}^{\dagger }]\) | Gaussian |
Squeezing | \(S(r,\phi )=\exp \left[\frac{r}{2}({e}^{-i\phi }{\hat{a}}^{2}-{e}^{i\phi }{\hat{a}}^{\dagger 2})\right]\) | Gaussian |
Beamsplitter | \(BS(\theta ,\phi )=\exp \left[\theta \left({e}^{i\phi }{\hat{a}}_{i}{\hat{a}}_{j}^{\dagger }-{e}^{-i\phi }{\hat{a}}_{i}^{\dagger }{\hat{a}}_{j}\right)\right]\) | Gaussian |
Quadratic Phase | \(P(s)=\exp \left[i\frac{s}{2\hslash }{x}^{2}\right]\) | Gaussian (Decomposable) |
Controlled-Phase | \(CZ(s)=\exp \left[is\frac{{\hat{x}}_{i}{\hat{x}}_{j}}{\hslash }\right]\) | Gaussian (Decomposable) |
Two-mode squeezing | \({S}_{2}(z)=\exp \left[\,z{\hat{a}}_{i}^{\dagger }{\hat{a}}_{j}^{\dagger }-{z}^{* }{\hat{a}}_{i}{\hat{a}}_{j}\right]\) | Gaussian (Decomposable) |
Cubic Phase | \(V(\gamma )=\exp \left[i\frac{\gamma }{3\hslash }{\hat{x}}^{3}\right]\) | Non-Gaussian |
Kerr | \(K(\kappa )=\exp \left[i\kappa {\hat{n}}^{2}\right]\) | Non-Gaussian |
Cross-Kerr | \(CK(\kappa )=\exp \left[i\kappa {\hat{n}}_{i}{\hat{n}}_{j}\right]\) | Non-Gaussian |
