This class provides an efficient implementation of ladder term operators, i.e., operators of the form
\[O=\sum\limits_{j}\alpha_jO_j \]
where each term \(O_j\) is a product of fermionic raising \(a_i^{\dagger}\) and lowering \(a_i\) operators acting on the \(i\) th fermionic mode.
The ladder operators satisfy the commutation relations
\[\begin{split}\{a_i,a_j^{\dagger}\} &= a_ia_j^{\dagger}+a_j^{\dagger}a_i = \delta_{ij}\\ \{a_i^{\dagger},a_j^{\dagger}\} &= \{a_i,a_j\} = 0\end{split}\]
Examples
A ladder term operator can be specified conveniently in terms of a (lowering, i.e., annihilation), c (raising, i.e., creation) operators:
from qrisp.operators.fermionic import a, c O = a(2)*c(1)+a(3)*c(2) O
Yields \(a_2c_1+a_3c_2\).
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