Measuring tensor products of Pauli operators

Question

Is there a neat way to derive and efficiently implement a measurement circuit for tensor products of arbitrary Pauli operators like $XZZXZ$ in Qiskit ?

I tried using the pauli_measurement function, where I used a PauliOperator object initialized from a corresponding label, but this function seems to perform single-qubit post-rotations for each part of the label and I am not sure if this is what I actually want to measure. I assume, that a generalization of what is described here https://github.com/MicrosoftDocs/quantum-docs/blob/main/articles/concepts-pauli-measurements.md would fit this measurement scenario.

Answer 1

If you don't want to write your own function to do this then one way to do this is through qiskit pauli_measurement.

For example:

from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister 
from qiskit.quantum_info import Pauli
from qiskit.aqua.operators.legacy import pauli_measurement
qr = QuantumRegister(4)
cr = ClassicalRegister(4)
qc = QuantumCircuit(qr,cr)
pauli_measurement(qc, Pauli('XYZX'), qr , cr  )
print(qc)

      ┌───┐       ┌─┐        
q2_0: ┤ H ├───────┤M├────────
      └┬─┬┘       └╥┘        
q2_1: ─┤M├─────────╫─────────
       └╥┘ ┌─────┐ ║ ┌───┐┌─┐
q2_2: ──╫──┤ SDG ├─╫─┤ H ├┤M├
        ║  └┬───┬┘ ║ └┬─┬┘└╥┘
q2_3: ──╫───┤ H ├──╫──┤M├──╫─
        ║   └───┘  ║  └╥┘  ║ 
c2: 4/══╩══════════╩═══╩═══╩═
        1          0   3   2