qml.qchem.particle_number

particle_number(orbitals)

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 * I(0)
  + -0.5 * Z(0)
  + -0.5 * Z(1)
  + -0.5 * Z(2)
  + -0.5 * Z(3)
)

code/api/pennylane.qchem.particle_number

 

Download Python script

 

Download Notebook

 

View on GitHub