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I am trying to compute the ground state energy of He-He using VQE. For this purpose I have utilized Qskit and have written the following script:

from qiskit.chemistry.drivers import PySCFDriver, UnitsType, Molecule
from qiskit.chemistry.transformations import FermionicTransformation, FermionicQubitMappingType
from qiskit.aqua.algorithms import NumPyMinimumEigensolver
from qiskit import BasicAer
from qiskit.aqua import QuantumInstance
from qiskit.chemistry.algorithms.ground_state_solvers.minimum_eigensolver_factories import VQEUCCSDFactory
from qiskit.aqua.algorithms import VQE
from qiskit.circuit.library import TwoLocal
from qiskit.chemistry.algorithms.ground_state_solvers import GroundStateEigensolver

molecule = Molecule(geometry=[['He', [0., 0., 0.]],
                              ['He', [0., 0., 3.1]]],
                     charge=0, multiplicity=1)

driver = PySCFDriver(molecule = molecule, unit=UnitsType.ANGSTROM, basis='sto3g')
transformation = FermionicTransformation(qubit_mapping=FermionicQubitMappingType.JORDAN_WIGNER)

numpy_solver = NumPyMinimumEigensolver()
vqe_solver = VQEUCCSDFactory(QuantumInstance(BasicAer.get_backend('statevector_simulator')))


num_qubits = 4
tl_circuit = TwoLocal(num_qubits, ['h', 'rx'], 'cz',
                      entanglement='full', reps=3, parameter_prefix = 'y')

tl_circuit.draw(output = 'mpl')

another_solver = VQE(var_form = tl_circuit,
                     quantum_instance = QuantumInstance(BasicAer.get_backend('statevector_simulator')))


calc = GroundStateEigensolver(transformation, vqe_solver)
res = calc.solve(driver)

print(transformation)
print(res)

When I run it I get a following error message:

Traceback (most recent call last):
  File "test_remove.py", line 37, in <module>
    res = calc.solve(driver)
  File "/Users/monica/miniconda3/lib/python3.7/site-packages/qiskit/chemistry/algorithms/ground_state_solvers/ground_state_eigensolver.py", line 94, in solve
    solver = self._solver.get_solver(self.transformation)
  File "/Users/monica/miniconda3/lib/python3.7/site-packages/qiskit/chemistry/algorithms/ground_state_solvers/minimum_eigensolver_factories/vqe_uccsd_factory.py", line 212, in get_solver
    same_spin_doubles=self._same_spin_doubles)
  File "/Users/monica/miniconda3/lib/python3.7/site-packages/qiskit/chemistry/components/variational_forms/uccsd.py", line 153, in __init__
    excitation_type=self._excitation_type,)
  File "/Users/monica/miniconda3/lib/python3.7/site-packages/qiskit/chemistry/components/variational_forms/uccsd.py", line 509, in compute_excitation_lists
    raise ValueError('No unoccupied orbitals')
ValueError: No unoccupied orbitals

Can anyone explain to me what is going on? What am I doing wrong?

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Try this:

from qiskit import IBMQ
from qiskit.aqua import QuantumInstance
from qiskit.aqua.components.optimizers import COBYLA
from qiskit.aqua.algorithms import VQE
from qiskit.circuit.library import TwoLocal
from qiskit.chemistry.qmolecule import QMolecule
from qiskit.chemistry.drivers import PySCFDriver, UnitsType
from qiskit.chemistry import FermionicOperator
from qiskit.chemistry.core import Hamiltonian, TransformationType, QubitMappingType

import warnings
warnings.filterwarnings("ignore",category=DeprecationWarning)


##### Defining Molecular Structure #######
atom_structure = "He 0. 0. 0.; He 3.1 0. 0"  
[unit, charge, spin, basis]= [UnitsType.ANGSTROM, 0, 0, 'sto3g'] 
driver = PySCFDriver(atom= atom_structure, unit=unit,charge=charge, spin=spin, basis=basis)
qmolecule = driver.run()
ferOp = Hamiltonian(transformation = TransformationType.FULL , 
                    qubit_mapping = QubitMappingType.PARITY,
                    two_qubit_reduction = True,
                    freeze_core = True, 
                    orbital_reduction = [ ], 
                    z2symmetry_reduction = None)
qubitOp, aux_ops = ferOp.run(qmolecule)
print( qubitOp.print_details() )

##### Exact Diagonalization Result ########
from qiskit.aqua.algorithms import NumPyMinimumEigensolver
exact_result = NumPyMinimumEigensolver(qubitOp).run() 
print('THis is the exact result:', exact_result)


##### VQE Result #######
tl_circuit = TwoLocal(qubitOp.num_qubits, ['h', 'rx'], 'cz',
                      entanglement='full', reps=3, parameter_prefix = 'y')
provider = IBMQ.load_account()
backend = provider.get_backend('ibmq_qasm_simulator')
quantum_instance = QuantumInstance(backend,
                                   shots = 8192,
                                   initial_layout = None,
                                   optimization_level = 3)  

optimizer = COBYLA(maxiter= 100,tol=0.000000001)   
vqe = VQE(qubitOp, tl_circuit, optimizer,initial_point= None)
vqe_result = vqe.run(quantum_instance)
vqe_result

Note that by specifying freeze_core = True and z2symmetry_reduction = 'auto' will help with reducing the number of qubits needed to solve your problem.

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    $\begingroup$ Thank you! It helps a lot. I am wondering if it is possible to run a quantum simulation just for an atom. I made a modification of "atom_structure", and left only he, but it leads to errors. I assume that the circuit must be defined differently. Do you have any experience with this? $\endgroup$
    – user14660
    Jan 31 at 16:53
  • $\begingroup$ You are welcome. It should be possible, but you end up with 0 qubits because of the two_qubit_reduction method... but you can turn this off and having a two qubit system to play with. That is, you can just replace the ferOp line with this: ferOp = Hamiltonian(transformation = TransformationType.FULL , qubit_mapping = QubitMappingType.PARITY, two_qubit_reduction = False, freeze_core = True, orbital_reduction = [ ], z2symmetry_reduction = None) $\endgroup$
    – KAJ226
    Jan 31 at 18:09
  • $\begingroup$ The Ansatze (parametrized quantum circuit) will update itself so you don't have to worry make any changes there. $\endgroup$
    – KAJ226
    Jan 31 at 18:12
  • $\begingroup$ It worked for the he atom! Thanks again! I tested the code for a hydrogen atom and I am getting an error from the pyscf side:File "/Users/monica/miniconda3/lib/python3.7/site-packages/pyscf/ao2mo/incore.py",line 65, in full return general(eri_ao, (mo_coeff,)*4, verbose, compact) File "/Users/monica/miniconda3/lib/python3.7/site-packages/pyscf/ao2mo/incore.py", line 125, in general if eri_ao.size == nao**4: AttributeError: 'NoneType' object has no attribute 'size Do you reproduce this issue? I also ran a test for Li, and I do not observe any problems. Not sure what is going on. $\endgroup$
    – user14660
    Jan 31 at 19:46
  • $\begingroup$ @user14660 for problems with pyscf you might also try materials.stackexchange.com where they have a tag just for pyscf. $\endgroup$ Mar 2 at 6:25

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