FermionicOperator#

class FermionicOperator(terms_dict={})[source]#

This class provides an efficient implementation of ladder term operators, i.e., operators of the form

O = \sum_{j} α_{j} O_{j}

where each term $O_{j}$ is a product of fermionic raising $a_{i}^{†}$ and lowering $a_{i}$ operators acting on the $i$ th fermionic mode.

The ladder operators satisfy the commutation relations

\begin{aligned} {a_{i}, a_{j}^{†}} & = a_{i} a_{j}^{†} + a_{j}^{†} a_{i} = δ_{i j} \\ {a_{i}^{†}, a_{j}^{†}} & = {a_{i}, a_{j}} = 0 \end{aligned}

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 $a_{2} c_{1} + a_{3} c_{2}$ .

Methods#

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