# CubicPhase gate

The CubicPhase gate in the CV model is described as

What does x hat signify?

Hey @sophchoe! \hat{x} here means the position operator.

I understand that. However, your Strawberry Fock device is based on the phase space representation with number basis |0>, |1>, … |n> which are functions of both the position and momentum variables.

How can you isolate just the position from number basis?

Good question! If I understand correctly, the position operator can be written as a linear combination of creation and annihilation operators:

\hat{x} \propto \hat{a} + \hat{a}^\dagger

where, for example,

\hat{a}^\dagger \vert {n}\rangle = \sqrt{n+1} \vert {n+1} \rangle.

Now, the CubicPhase gate is just a function of the position operator, which also means it’s a function of the creation and annihilation operators. In that sense, the CubicPhase gate’s action on number-basis states is well-defined!

@isaacdevlugt

I didn’t know the first expression. Now it makes perfect sense!!! Thank you.

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