FermionicOperator

class FermionicOperator(terms_dict={})

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 \(a_2c_1+a_3c_2\).

Methods

FermionicOperator.dagger()	Returns the daggered/adjoint version of self.
FermionicOperator.hermitize()	Returns the hermitized version of self.
FermionicOperator.ground_state_energy()	Calculates the ground state energy (i.e., the minimum eigenvalue) of the operator classically.
FermionicOperator.from_pyscf(...)
FermionicOperator.reduce([assume_hermitian])	Applies the fermionic anticommutation laws to bring the operator into a standard form.
FermionicOperator.get_measurement(qarg[, ...])	This method returns the expected value of a Hamiltonian for the state of a quantum argument.
FermionicOperator.to_qubit_operator([...])	Transforms the FermionicOperator to a QubitOperator.
FermionicOperator.trotterization([t, steps, ...])	Returns a function for performing Hamiltonian simulation, i.e., approximately implementing the unitary operator \(e^{itH}\) via Trotterization.