qiskit: How to get an operator acting on a certain qubit?

Question

I have a system of $N$ qubits and want to construct a quantum operator $Z_i Z_j + Z_k$, where $Z_i$ denotes the Pauli-Z operator acting on the $i$th qubit. Is there any direct way in qiskit, how I could implement this?
I know that I can construct an operator by e.g. saying op = Z^Z, if I have a system of 2 qubits and want the operator being the Pauli-Z on each qubit. But I would like to tell qiskit the indices of the qubits that $Z$ should act on (such that on all the other qubits Identity is applied).
My way so far consists of constructing a Quantum Circuit and converting this to an operator by
circZZ = QuantumCircuit(N)  # circuit for Z_i Z_j
circZ = QuantumCircuit(N)  # circuit for Z_k
circZZ.z(i)
circZZ.z(j)
circZ.z(k)
opZZ = CircuitOp(circZZ)  # convert circuit to operator
opZ = CircuitOp(circZ)  # convert circuit to operator
op = opZZ + opZ

But that means I have to create quantum circuits everytime I want to get this operator. Is there any shorter and more elegant way to create such an operator?

luciano · Accepted Answer

The class Operator has a from_label method: https://qiskit.org/documentation/stubs/qiskit.quantum_info.Operator.html?highlight=operator%20from_label#qiskit.quantum_info.Operator.from_label
That means you could do something like this:
opZZ = Operator.from_label('ZZ')
opZ = Operator.from_label('Z')

It's possible to add opZZ and opZ into N-sized op. However, you have to call the _add by hand:
op = 0 * Operator.from_label('I' * N)  # Set the initial operator to zero
op = op._add(opZZ, qargs=[i,j])
op = op._add(opZ, qargs=[k])

Cryoris · Answer

You could use the feature that the Opflow in Aqua can take integers as tensorpower, like Z ^ 5 and then fill the blanks with identities.
In a short function that could look like
from qiskit.aqua.operators import Z, I

def get_term(i, j, k, n):
    """i, j and k as in your description and n is the number of qubits."""
    zz = (I ^ i) ^ Z ^ (I ^ j - i - 1) ^ Z ^ (I ^ (n - j - i - 1))
    z = (I ^ k) ^ Z ^ (I ^ (n - k - 1))
    return zz + z

print(get_term(0, 2, 4, 5))
# 1.0 * ZIZII
# + 1.0 * IIIIZ

Note that the order of Z's is reversed to what you did with the circuits, so to get the same results you can just call
get_term(n - i - 1, n - j - 1, n - k - 1, n)

But this is just one way to get to the result, I'm sure there are many others! Your method, via circuits, is looks perfectly good to me.

qiskit: How to get an operator acting on a certain qubit?

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