How to use VQE function in Qiskit

Question

As part of a project I'm working on, I want to use VQE algorithm to calculate the minimal eigenvalue for given Hamiltonian. I use Qiskit on IBM UI online.

The Hamiltonian is given as a sum of tensor products

$H = Z\otimes Z + Z \otimes X + ...$

I don't understand two main points:

1. How should I pass the Hamiltonian to the VQE? should I pass it as a list? i.e. $ H = [Z\^Z, X\^Z]$?
2. I understand that I need to create N circuits, where N is the number of tensor products which constitute the Hamiltonian, so that each circuit will handle another part of the Hamiltonian. Do I understand this correctly?

Thank you.

Answer 1

In the latest version of qiskit (package aqua has been deprecated and had a massive refactoring) it is enough to import the base Pauli matrices X, Y, Z from qiskit opflow and perform the tensor product in the way you want, i.e.,

from qiskit.opflow import X,Y,Z,I   
operator = Z ^ Z + X ^ X

Afterwards, you initialize VQE

from qiskit.algorithms import VQE
vqe = VQE(ansatz=your_ansatz, quantum_instance=your_quantum_instance, optimizer=your_optimizer)

And execute it (note that in the latest version VQE belongs to qiskit.algorithms package and the paramter var_form has been renamed in ansatz):

vqe.compute_minimum_eigenvalue(matrix_op).eigenvalue

Clearly, I am assuming that you are interested in the eigenvalue, but there are other return values that you can retrieve. For a full reference:

https://qiskit.org/documentation/stubs/qiskit.algorithms.VQE.html

Answer 2

Try this:

from qiskit.aqua.operators import WeightedPauliOperator
dict = {
    'paulis': [{"coeff": {"imag": 0.00, "real": 1 }, "label": "ZZ" },
              {"coeff": {"imag": 0.00, "real": 1 }, "label": "XX" }
              ]
}
Operator = WeightedPauliOperator.from_dict(dict)

Now you can pass this operator to your VQE call:

VQE(operator= Operator, var_form= ... )