How is a linear combination of pauli operators applied to a quantum circuit in qiskit?

Question

Consider a quantum circuit of 2 qubit:

quantumcircuit = QuantumCircuit(2)

If one wishes to apply a Pauli-X operator to the first qubit, one writes: quantumcircuit.x(0)

But how should it be written programmatically if the wish is to apply a Bell measurement bases $\frac{1}{\sqrt{2}}[X - Z]$?

Answer 1

The operation $\frac{1}{\sqrt{2}}[X - Z]$ is unitary. You can easily check that:

from qiskit.quantum_info import SparsePauliOp
import numpy as np

op = SparsePauliOp(['X', 'Z'], [1 / np.sqrt(2), -1 / np.sqrt(2)])
print(op.is_unitary())

So, you can add it to your circuit using QuantumCircuit.unitary() method:

quantumcircuit.unitary(op, [0])