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group_terms_by_electronic_structure

group_terms_by_electronic_structure(op, num_modes, *, two_body_physicist_order=False)

Groups the terms of an operator by their electronic structure.

This function automatically populates the groups attribute of the provided FermionOperator such that terms satisfying a symmetric perturbation present in electronic-structure Hamiltonians are grouped.

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.

More concretely, given an electronic-structure Hamiltonian of the form

H=∑ijcijai†aj+∑ijklcijklai†aj†akal ,\mathcal{H} = \sum_{ij} c_{ij} a^\dagger_i a_j + \sum_{ijkl} c_{ijkl} a^\dagger_i a^\dagger_j a_k a_l \, ,

this function will group 1-body terms with permutational symmetry of (i, j) as well as the 2-body terms with permutational symmetry of (i, j, k, l). For the 2-body terms, not all permutations will be grouped. Instead, the two_body_physicist_order determines how the four indices get grouped into pairs of two within which permutational symmetries exist:

  • two_body_physicist_order=False (default): (i, l) and (j, k)
  • two_body_physicist_order=True: (i, k) and (j, l)
from qiskit_fermions.operators import FermionOperator
from qiskit_fermions.operators.library import FCIDump

fcidump = FCIDump.from_file("molecule.fcidump")
operator = FermionOperator.from_fcidump(fcidump)

normal = op.normal_ordered().simplify(atol=0.0)

group_terms_by_electronic_structure(normal, 2 * fcidump.norb, two_body_physicist_order=False)

assert normal.has_groups()

Parameters

  • op – the normal-ordered operator whose terms to group.
  • num_modes – the number of spin-less fermionic modes in the system.
  • two_body_physicist_order – whether the 2-body terms are stored in physicists order.

Raises

ValueError – if an unexpected term is encountered.