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
- 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