qrunch.quantum.operators.second_quantization.fermion

Module that contains the abstract fermion operators \(\hat{a}\) and \(\hat{a}^{\dagger}\).

A general second quantized fermionic Hamiltonian operator can be expressed as a combination of these fundamental operators through addition and multiplication, applied to specific qubits.

Example

from qrunch.quantum.operators.second_quantization.fermion import FermionCreation, FermionAnnihilation

Obs = 0.5 * FermionCreation(1) * FermionAnnihilation(1)
- 0.7 * FermionCreation(1) * FermionCreation(2) * FermionAnnihilation(3) * FermionAnnihilation(4)

A Hamiltonian like this can then be mapped to Pauli operators (which can be used in e.g. estimators), by using e.g. the Jordan-Wigner mapper.

Classes

`FermionAnnihilation`	Fermion annihilation operator acting on a specific site.
`FermionCreation`	Fermion creation operator acting on a specific site.

class FermionAnnihilation

Bases: FermionOperator

Fermion annihilation operator acting on a specific site.

__init__(site: AbstractIndex | int) → None

Initialize the fermion operator on a specific site.

Parameters:: site (AbstractIndex | int) – The site to act upon.
Return type:: None

get_indices() → tuple[AbstractIndex | int]

Get indices of the operator.

Returns: Indices of the operator

Return type:: tuple[AbstractIndex | int]

property site: AbstractIndex | int: The site the operator acts on.

with_indices(index_value_pairs: IndexValuePairs) → FermionOperator

Create a new copy of the operator with the AbstractIndex set to the given value.

Parameters:: index_value_pairs (IndexValuePairs) – Map of abstract indices to concrete values.
Return type:: FermionOperator

Returns: New copy of the operator with the AbstractIndex set to the given value.

class FermionCreation