CubicPhase gate

The CubicPhase gate in the CV model is described as 17%20PM

What does x hat signify?

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

Hi @isaacdevlugt

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.

1 Like

Nice! :grin: Glad I could help :smiley:

@isaacdevlugt

NIST is active with quantum memory research. Adding the memory component to Xanadu’s QPU will greatly help with complex operational circuits. (I apologize if I’ve posted this to Catalina already.)