Applying Jordan-Wigner to FermionOperator vs. InteractionOperator

[max-radin]

In some cases the result of a Jordan-Wigner transform applied to an InteractionOperator is different if it is converted to a FermionOperator first, as shown in the code below. It seems like jordan_wigner_interaction_op only gives the correct result for Hermitian operators.

from openfermion.ops import InteractionOperator
from openfermion.transforms import get_fermion_operator, jordan_wigner
import numpy as np

N = 4
kappa = np.zeros((N, N))
kappa[0,3] = 2.0
op = InteractionOperator(0., -kappa, np.zeros((N, N, N, N)))

qubit_op1 = jordan_wigner(op)
print(qubit_op1)
# -0.5 [X0 Z1 Z2 X3] +
# -0.5 [Y0 Z1 Z2 Y3]

qubit_op2 = jordan_wigner(get_fermion_operator(op))
print(qubit_op2)
# (-0.5+0j) [X0 Z1 Z2 X3] +
# -0.5j [X0 Z1 Z2 Y3] +
# 0.5j [Y0 Z1 Z2 X3] +
# (-0.5+0j) [Y0 Z1 Z2 Y3]

[kevinsung]

Indeed, jordan_wigner_interaction_op is only guaranteed to work for Hermitian operators and is optimized based on that assumption. The InteractionOperator class is intended to represent only Hermitian operators, even though this is neither documented nor enforced. @babbush or @jarrodmcc can correct me if I'm wrong. I think we need to document this better; enforcement would be tricky, though there are certainly things we can do to help (e.g. #444 ).

[babbush]

Yes, so I think we just need better documentation here.