Add from_fermion_operator method to MoelcularHamiltonian class

[miamico]

Add the feature to define a Molecular Hamiltonian from a Fermion Operator

Closes #385

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[miamico]

This will close issue #385

[kevinsung]

This needs a test.

[miamico]

Do you think something like the following would work as a test?

norb = 10

rng1 = np.random.default_rng(0) 

# generate a random molecular hamiltonian 
mol_hamiltonian = ffsim.random.random_molecular_hamiltonian(norb=norb, seed=rng1)

# convert to fermion op
mol_hamiltonian_fops = ffsim.fermion_operator(mol_hamiltonian)
mol_hamiltonian_fops.normal_ordered()
mol_hamiltonian_fops.simplify()

# convert back from fermion op to ham
mol_hamiltonian_from_ferm = molecular_hamiltonian_from_fermion_operator(mol_hamiltonian_fops)


# check they are matching
tol = 1e-8
assert abs(mol_hamiltonian.constant - mol_hamiltonian_from_ferm.constant) < tol, "Constant mismatch!"
assert np.allclose(mol_hamiltonian.one_body_tensor, mol_hamiltonian_from_ferm.one_body_tensor, atol=tol), "One‑body mismatch!"
assert np.allclose(mol_hamiltonian.two_body_tensor, mol_hamiltonian_from_ferm.two_body_tensor, atol=tol), "Two‑body mismatch!"

[kevinsung]

Do you think something like the following would work as a test?

norb = 10

rng1 = np.random.default_rng(0) 

# generate a random molecular hamiltonian 
mol_hamiltonian = ffsim.random.random_molecular_hamiltonian(norb=norb, seed=rng1)

# convert to fermion op
mol_hamiltonian_fops = ffsim.fermion_operator(mol_hamiltonian)
mol_hamiltonian_fops.normal_ordered()
mol_hamiltonian_fops.simplify()

# convert back from fermion op to ham
mol_hamiltonian_from_ferm = molecular_hamiltonian_from_fermion_operator(mol_hamiltonian_fops)


# check they are matching
tol = 1e-8
assert abs(mol_hamiltonian.constant - mol_hamiltonian_from_ferm.constant) < tol, "Constant mismatch!"
assert np.allclose(mol_hamiltonian.one_body_tensor, mol_hamiltonian_from_ferm.one_body_tensor, atol=tol), "One‑body mismatch!"
assert np.allclose(mol_hamiltonian.two_body_tensor, mol_hamiltonian_from_ferm.two_body_tensor, atol=tol), "Two‑body mismatch!"

Yes, but I don't think we should do the normal ordering.