Get the inverse of a Hermitian operator for measurement in qiskit

Question

I am using Qiskit to measure the Hamiltonian H, which isbasically sum of Pauli strings, say something like 2*X^X+0.5*Z^Y. For one variable, I need to get the analytically form of the inverse of H. It seems that there is no easy way to directly get the inverse observable. So, I am wondering that how can I get this done by using qiskit?

Answer 1

It seems that Qiskit does not have this feature. However, you can get the matrix, inverse it using numpy.linalg.inv(), then convert it to operator object again:

from qiskit.opflow import X, Y, Z
from qiskit.opflow.primitive_ops import MatrixOp
import numpy as np

op = 2*(X^X)+0.5*(Z^Y)
inv_matrix = np.linalg.inv(op.to_matrix())
operator = MatrixOp(inv_matrix)

print(operator.to_pauli_op())

And to get a PauliSumOp:

pauli_list = [(p.primitive.to_label(), p.coeff) for p in operator.to_pauli_op().oplist]

pauli_sum_op = PauliSumOp.from_list(pauli_list)