# qml.qchem.particle_number¶

particle_number(orbitals)[source]

Compute the particle number observable $$\hat{N}=\sum_\alpha \hat{n}_\alpha$$ in the Pauli basis.

The particle number operator is given by

$\hat{N} = \sum_\alpha \hat{c}_\alpha^\dagger \hat{c}_\alpha,$

where the index $$\alpha$$ runs over the basis of single-particle states $$\vert \alpha \rangle$$, and the operators $$\hat{c}^\dagger$$ and $$\hat{c}$$ are the particle creation and annihilation operators, respectively.

Parameters

orbitals (int) – Number of spin orbitals. If an active space is defined, this is the number of active spin-orbitals.

Returns

the particle number observable

Return type

pennylane.Hamiltonian

Raises

ValueError – If orbitals is less than or equal to 0

Example

>>> orbitals = 4
>>> print(particle_number(orbitals))
(2.0) [I0]
+ (-0.5) [Z0]
+ (-0.5) [Z1]
+ (-0.5) [Z2]
+ (-0.5) [Z3]


Using PennyLane

Development

API