How can I obtain the numerical values of the density matrix elements in a state_city plot in qiskit

Question

I have run code following the documentation in the qiskit section on Entanglement Verification, up through the steps:

[Earlier material from Entanglement Verification, followed by]

meas_calibs, state_labels = complete_meas_cal(qubit_list=qubit_list, qr=qr, circlabel='mcal')
job_c = execute(meas_calibs, backend=qcomp, coupling_map=coupling_map)
job_monitor(job_c)
meas_result = job_c.result()

meas_fitter = CompleteMeasFitter(meas_result,state_labels,circlabel='mcal')
result_em = meas_fitter.filter.apply(job.result())
tomo_em = StateTomographyFitter(result_em, qst)
visualization.plot_state_city(tomo.fit(),"Density Matrix")

This prints a very useful plot showing the real and imaginary parts of the density matrix, so it seems to be working.

Question: How can I print the actual numerical values of the density matrix elements that are being plotted?

Thanks in advance for any help!

Answer 1

As far as I know, this is not yet possible in qiskit, since the plot_state_city function does not accept an optional argument that would help doing this.

However, this function returns a Figure object from matplotlib, which one can access. Thus, it is possible to modify the plot once it has been created with the plot_state_city option to place the labels where we want.

First of all, we create the circuit:

qc = QuantumCircuit(2)
qc.h(0)
qc.cnot(0, 1)
qc.s(0)

and we create the associated density matrix, were we to apply this circuit on the $|00\rangle$ state:

dm = qi.DensityMatrix.from_instruction(qc)

Since we will need the real and imaginary parts of this matrix, we save them in a list:

arrays = [np.real(dm), np.imag(dm)]

And in order to get beautiful labels, we want their value to be printed using $\LaTeX$. For this, we can use the array_to_latex function from qiskit.visualize:

latex_sources = [array_to_latex(array, source=True) for array in arrays]

We also need to create the Figure object using plot_state_city:

ax = plot_state_city(dm)

And now the dirty hack begins. You can parse the source using vanilla Python to get the associated $\LaTeX$ labels to the value you want. The code for this is:

for index_source, latex_source in enumerate(latex_sources): 
    for index_line, line in enumerate(latex_source.split("\n")[3:-2]):
        for index_column, value in enumerate(line.split("&")):
            # Print label only if it is non-zero
            if arrays[index_source][index_line, index_column]:
                ax.axes[index_source].text(
                    index_column,
                    index_line,
                    arrays[index_source][index_line, index_column],
                    "$" + value.replace("\\\\", "").replace("tfrac", "dfrac") + "$"
                )

The final complete code is:

import qiskit.quantum_info as qi
from qiskit.visualization import plot_state_city, array_to_latex

def plot_state_city_with_labels(dm):
    ax = plot_state_city(dm)
    arrays = [np.real(dm), np.imag(dm)]
    latex_sources = [array_to_latex(array, source=True) for array in arrays]
    offset_x = 0
    offset_y = 0

    for index_source, latex_source in enumerate(latex_sources): 
        for index_line, line in enumerate(latex_source.split("\n")[3:-2]):
            for index_column, value in enumerate(line.split("&")):
                # Print label only if it is non-zero
                if arrays[index_source][index_line, index_column]:
                    ax.axes[index_source].text(
                        index_column,
                        index_line,
                        arrays[index_source][index_line, index_column],
                        "$" + value.replace("\\\\", "").replace("tfrac", "dfrac") + "$"
                    )
    return ax

qc = QuantumCircuit(2)
qc.h(0)
qc.cnot(0, 1)
qc.s(0)
dm = qi.DensityMatrix.from_instruction(qc)
plot_state_city_with_labels(dm)

which results in the following plot:

However, it might be worth a try to open an issue on the qiskit-terra GitHub to add such a feature.