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In this excellently answered question 'How are gates implemented in a continuous-variable quantum computer?' the typical gates for CV quantum computing were listed and described. In particular for almost all the gates there is a description of their resulting effects on the quadrature position ($X$) and momentum ($P$).

The exception is with the action of the Kerr hamiltonian (whose action is also not described explicitely on the quadratures in the original paper by Lloyd either). There is likely a reason for this but all the same my question is:

What is the action of the Kerr hamiltonian, or a non linear equivalent like the cubic gate, on the quadratures (in the sense that the translation with P sends $x$ to $x+t$ or the squeeze gate $x$ to $xe^t$ etc)?

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  • $\begingroup$ Why not work it out yourself? If you understood the answer to the question you provided the link to, you should be perfectly able to compute the actions. Hint: for the Kerr Hamiltonian you should find an infinite series, for the cubic Hamiltonian $H=X^3/3$, you can find a nice closed form. $\endgroup$
    – Marsl
    Commented May 5, 2020 at 8:54

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