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.


2 Answers 2


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):


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:


  • $\begingroup$ Hi @Vindem, what is this matrix_op in the last line? It would be great if you can explain. $\endgroup$
    – Manu
    Mar 15 at 21:50
  • $\begingroup$ By matrix_op do you mean operator? $\endgroup$
    – Manu
    Mar 15 at 21:56

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= ... )
  • $\begingroup$ Thank you for your comment. After few trials it appears that the expression doesn't need to be modified but needs to be passed as it is $\endgroup$ Oct 15, 2020 at 4:48

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