I'm trying to reproduce the results of this article https://arxiv.org/abs/1801.03897, using Qiskit and Xanadu PennyLane.
Particularly, this part with expected values of the Pauli operators:
For Ansatz circuit from the mentioned article
I can get the same results for $\langle Z_0 \rangle$ and $\langle Z_1 \rangle$ but not for $\langle X_0X_1 \rangle$, $\langle Y_0Y_1 \rangle$. I calculate expected values in the following way:
$$\langle Z_0 \rangle = P(q_0=0)-P(q_0=1),$$ $$\langle Z_1 \rangle = P(q_0=0)-P(q_0=1).$$
And for a product of the Pauli matrices: $$\langle X_0X_1 \rangle = [P(q_0=0)-P(q_0=1)]*[P(q_1=0)-P(q_1=1)],$$ $$\langle Y_0Y_1 \rangle = [P(q_0=0)-P(q_0=1)]*[P(q_1=0)-P(q_1=1)],$$
where $P(q_0=0)$ is probability of getting qubit 0 in state $|0\rangle$ and $P(q_0=1)$ is probability of getting qubit 0 in state $|1\rangle$.
In Qiskit for $\langle X_0X_1 \rangle$, $\langle Y_0Y_1 \rangle$ I use pre-measurement single-qubit rotations $H$ and $R_x(-\pi/2)$ respectively.
Help me understand, where I could make a mistake?