openfermion.transforms.weyl_polynomial_quantization

View source on GitHub

Apply the Weyl quantization to a phase space polynomial.

openfermion.transforms.weyl_polynomial_quantization(
    polynomial
)

Used in the notebooks

The Weyl quantization is performed by applying McCoy's formula directly to a polynomial term of the form q^m p^n:

$q^m p^n -> (1/ 2^n) sum_{r=0}^{n} Binomial(n, r) \hat{q}^r \hat{p}^m q^{n-r}$

where q and p are phase space variables, and \hat{q} and \hat{p} are quadrature operators.

The input is provided in the form of a string, for example

.. code-block:: python

weyl_polynomial_quantization('q0^2 p0^3 q1^3')

where 'q' or 'p' is the phase space quadrature variable, the integer directly following is the mode it is with respect to, and '^2' is the polynomial power.