Fermi-Hubbard Model block/interleaved inconsistency

[ialsina]

Environment

• Qiskit Nature version: 343d290
• Python version: 3.9.16
• Operating system: RHEL 8.8

What is happening?

Since the introduction of InterleavedQubitMapper (#1046) the FermiHubbardModel class doesn't behave consistently with this feature, producing an interleaved-encoded hamiltonian when used together with JordanWignerMapper, and a block-encoded hamiltonian when used together with InterleavedQubitMapper.

How can we reproduce the issue?

>>> from qiskit_nature import settings
>>> from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
>>> from qiskit_nature.second_q.hamiltonians.lattices import LineLattice
>>> from qiskit_nature.second_q.mappers import JordanWignerMapper, InterleavedQubitMapper
>>> settings.use_pauli_sum_op = False

>>> lattice = LineLattice(2)
>>> model = FermiHubbardModel(
    lattice.uniform_parameters(
        uniform_interaction=-1.,
        uniform_onsite_potential=0.
    ),
    onsite_interaction=1.
)
>>> hamiltonian = model.second_q_op().simplify()
>>> print(hamiltonian)

FermionicOp({'+_0 -_2': (-1+0j), '-_0 +_2': (1+0j), '+_1 -_3': (-1+0j), '-_1 +_3': (1+0j), '+_0 -_0 +_1 -_1': (1+0j), '+_2 -_2 +_3 -_3': (1+0j)}, num_spin_orbitals=4, )

>>> mapper = JordanWignerMapper()
>>> print(mapper.map(hamiltonian)) # Block encoding

SparsePauliOp(['IYZY', 'IXZX', 'YZYI', 'XZXI', 'IIII', 'IIZI', 'IIIZ', 'IIZZ', 'ZIII', 'IZII', 'ZZII'],
              coeffs=[-0.5 +0.j, -0.5 +0.j, -0.5 +0.j, -0.5 +0.j,  0.5 +0.j, -0.25+0.j,
 -0.25+0.j,  0.25+0.j, -0.25+0.j, -0.25+0.j,  0.25+0.j])

>>> interleaved_mapper = InterleavedQubitMapper(mapper)
>>> print(interleaved_mapper.map(hamiltonian)) # Interleaved encoding

SparsePauliOp(['IIYY', 'IIXX', 'YYII', 'XXII', 'IIII', 'IZII', 'IIIZ', 'IZIZ', 'ZIII', 'IIZI', 'ZIZI'],
              coeffs=[-0.5 +0.j, -0.5 +0.j, -0.5 +0.j, -0.5 +0.j,  0.5 +0.j, -0.25+0.j,
 -0.25+0.j,  0.25+0.j, -0.25+0.j, -0.25+0.j,  0.25+0.j])

What should happen?

For consistency with the other uses of JordanWignerMapper and InterleavedQubitMapper, the outcomes of the prints should be:

>>> hamiltonian = model.second_q_op().simplify()
>>> print(hamiltonian)

FermionicOp({'+_0 -_1': (-1+0j), '-_0 +_1': (1+0j), '+_2 -_3': (-1+0j), '-_2 +_3': (1+0j), '+_0 -_0 +_2 -_2': (1+0j), '+_1 -_1 +_3 -_3': (1+0j)}, num_spin_orbitals=4, )

>>> mapper = JordanWignerMapper()
>>> print(mapper.map(hamiltonian)) # Block encoding

SparsePauliOp(['IIYY', 'IIXX', 'YYII', 'XXII', 'IIII', 'IZII', 'IIIZ', 'IZIZ', 'ZIII', 'IIZI', 'ZIZI'],
              coeffs=[-0.5 +0.j, -0.5 +0.j, -0.5 +0.j, -0.5 +0.j,  0.5 +0.j, -0.25+0.j,
 -0.25+0.j,  0.25+0.j, -0.25+0.j, -0.25+0.j,  0.25+0.j])

>>> interleaved_mapper = InterleavedQubitMapper(mapper)
>>> print(interleaved_mapper.map(hamiltonian)) # Interleaved encoding

SparsePauliOp(['IYZY', 'IXZX', 'YZYI', 'XZXI', 'IIII', 'IIZI', 'IIIZ', 'IIZZ', 'ZIII', 'IZII', 'ZZII'],
              coeffs=[-0.5 +0.j, -0.5 +0.j, -0.5 +0.j, -0.5 +0.j,  0.5 +0.j, -0.25+0.j,
 -0.25+0.j,  0.25+0.j, -0.25+0.j, -0.25+0.j,  0.25+0.j])

Any suggestions?

In qiskit_nature/second_q/hamiltonians/fermi_hubbard_model.py, change the "index" variables everywhere from index = 2 * node + spin to index = node + spin * num_nodes. I am happy to open a PR with this change!

[mrossinek]

I think unifying the behavior of the FermiHubbardModel with the block-ordering of the ElectronicEnergy class is a good idea! Please go ahead and open a PR as you had suggested 🙂