openfermion.transforms.weyl_polynomial_quantization
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.
Args |
polynomial
|
str
polynomial function of q and p of the form
'qi^m pj^n ...' where i,j are the modes, and m, n the powers.
|
Returns |
QuadOperator
|
the Weyl quantization of the phase space function.
|
Warning |
The runtime of this method is exponential in the maximum locality
of the original operator.
|
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Last updated 2024-04-26 UTC.
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