# filter_diagonal_terms

### filter_diagonal_terms(op)

Filters out the terms of an operator that are diagonal in the occupation-number basis.

This removes every term from the provided
[`FermionOperator`](qiskit_fermions.operators.FermionOperator.html.md#qiskit_fermions.operators.FermionOperator) that is a product of number operators
($a^\dagger_i a_i$). This includes the constant term (a product of zero number operators),
single number operators, as well as higher-order products such as
$n_i n_j = a^\dagger_i a^\dagger_j a_j a_i$.

#### HINT
A major motivation for filtering such terms arises during the time evolution of operators,
where such diagonal terms, do not affect the time evolution besides introducing a global
phase. Consequently, bitstrings sampled from a time evolved state remain unaffected.
Removing them is therefore recommended, for example when preparing an electronic-structure
Hamiltonian for the qDRIFT time evolution used by SqDRIFT, as it avoids an otherwise
unnecessary sampling overhead.

#### CAUTION
The provided operator *must* be normal-ordered! This is an underlying assumption of the
implementation that is *not* being verified. See
[`normal_ordered()`](qiskit_fermions.operators.FermionOperator.html.md#qiskit_fermions.operators.FermionOperator.normal_ordered) for how to get an operator
of that form.

#### NOTE
The operator is modified *in place*. If it tracks group indices (see
[`groups`](qiskit_fermions.operators.FermionOperator.html.md#qiskit_fermions.operators.FermionOperator.groups)), surviving terms retain their
relative grouping but the group indices are reassigned to a contiguous range starting from 0.
You must therefore *not* rely on the specific group index of any term being preserved across
a call to this function.

```pycon
>>> from qiskit_fermions.operators import FermionOperator
>>> from qiskit_fermions.operators.terms.filtering import filter_diagonal_terms
>>> op = FermionOperator.from_dict(
...     {
...         (): 1.0,  # constant (diagonal)
...         ((True, 0), (False, 0)): 2.0,  # n_0 (diagonal)
...         ((True, 0), (True, 1), (False, 1), (False, 0)): 3.0,  # n_0 n_1 (diagonal)
...         ((True, 0), (False, 1)): 4.0,  # a†_0 a_1 (off-diagonal)
...     }
... )
>>> filter_diagonal_terms(op)
>>> list(op.iter_terms())
[([(True, 0), (False, 1)], (4+0j))]
```

* **Parameters:**
  **op** – the normal-ordered operator whose diagonal terms to filter out.