Plot_hinton imaginary section displays incorrect elements

[dimple12M]

Environment

• Qiskit Terra version: 0.19.1
• Python version: 3.7.9
• Operating system: ios

What is happening?

In the Visualization section: plot_hinton It displays 2 plots : one for real and one for imaginary There are 2 issues:

1. The imaginary elements displays the elements incorrect for real and negative numbers.
2. The size of the square of the elements are not equal for the imaginary plot

How can we reproduce the issue?

What should happen?

We expect the following plot_hinton

Any suggestions?

We make few simple changes in the state_visualizaton.py file and we can obtain the correct plot for the imaginary section in the plot_hinton.

[HuangJunye]

The second part of this issue (The size of the square of the elements are not equal for the imaginary plot) will be fixed by https://github.com/Qiskit/qiskit-terra/pull/8447.

I am investigating in the first part of the issue. The hinton plot currently plots the matrix transversely. I am not sure if this is the expected behavior.

from qiskit.quantum_info import DensityMatrix
from qiskit.tools.visualization import plot_state_hinton

state = DensityMatrix(
    [
        [1,1],
        [-1,-0.5] 
    ])
plot_state_hinton(state)

produces

[dimple12M]

The first part of the issue I think its related with the elements displayed on the hinton plot As seen from the density matrix, the elements of the real part is displayed as shown :

from qiskit import QuantumCircuit
from qiskit.quantum_info import DensityMatrix
from qiskit.visualization import plot_state_hinton

qc = QuantumCircuit(2)
qc.h(0)

state = DensityMatrix.from_instruction(qc)
print(state)

[dimple12M]

This the second example specific : elements related to real as well as imaginary section. I think, how are the elements are displaced is confusing . Still will look into it. Maybe we have can small description for the same.

from qiskit import QuantumCircuit
from qiskit.quantum_info import DensityMatrix
from qiskit.visualization import plot_state_hinton
![Screenshot 2022-08-10 at 4 10 46 PM](https://user-images.githubusercontent.com/65215560/183850058-45173b26-bbb1-4fa4-8186-e534dd6b726f.png)

state=DensityMatrix([[0.5+0.j, 0.+0.j, 0. -0.5j, 0. +0.j],
               [0.5+0.j, 0.+0.j, 0. -0.5j, 0. +0.j],
               [0.5 +0.j, 0. +0.j, 0. -0.5j, 0.+ 0.j],
               [0.5 +0.j, 0. +0.j, 0. -0.5j, 0. +0.j]])

plot_state_hinton(state)