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 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() for how to get an operator of that form.

Note

The operator is modified in place. If it tracks group indices (see 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.

>>> 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.