# cirq.scatter_plot_normalized_kak_interaction_coefficients

Plots the interaction coefficients of many two-qubit operations.

A point for the (x, y, z) normalized interaction coefficients of each interaction from the given interactions. The (x, y, z) coordinates are normalized so that the maximum value is at 1 instead of at pi/4.

If `include_frame` is set to True, then a black wireframe outline of the canonicalized normalized KAK coefficient space. The space is defined by the following two constraints:

``````0 <= abs(z) <= y <= x <= 1
if x = 1 then z >= 0
``````

The wireframe includes lines along the surface of the space at z=0.

The space is a prism with the identity at the origin, a crease along y=z=0 leading to the CZ/CNOT at x=1 and a vertical triangular face that contains the iswap at x=y=1,z=0 and the swap at x=y=z=1:

``````                     (x=1,y=1,z=0)
swap___iswap___swap (x=1,y=1,z=+-1)
_/\    |    /
_/   \   |   /
_/      \  |  /
_/         \ | /
_/            \|/
``````

(x=0,y=0,z=0) I---------------CZ (x=1,y=0,z=0)

`interactions` An iterable of two qubit unitary interactions. Each interaction can be specified as a raw 4x4 unitary matrix, or an object with a 4x4 unitary matrix according to `cirq.unitary` ( (e.g. `cirq.CZ` or a `cirq.KakDecomposition` or a `cirq.Circuit` over two qubits).
`include_frame` Determines whether or not to draw the kak space wireframe. Defaults to `True`.
`ax` A matplotlib 3d axes object to plot into. If not specified, a new figure is created, plotted, and shown.
`**kwargs` Arguments forwarded into the call to `scatter` that plots the points. Working arguments include color `c='blue'`, scale `s=2`, labelling `label="theta=pi/4"`, etc. For reference see the `matplotlib.pyplot.scatter` documentation: https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.scatter.html

The matplotlib 3d axes object that was plotted into.

``````>>> ax = None
>>> for y in np.linspace(0, 0.5, 4):
...     a, b = cirq.LineQubit.range(2)
...     circuits = [
...         cirq.Circuit(
...             cirq.CZ(a, b)**0.5,
...             cirq.X(a)**y, cirq.X(b)**x,
...             cirq.CZ(a, b)**0.5,
...             cirq.X(a)**x, cirq.X(b)**y,
...             cirq.CZ(a, b) ** 0.5,
...         )
...         for x in np.linspace(0, 1, 25)
...     ]
...     ax = cirq.scatter_plot_normalized_kak_interaction_coefficients(
...         circuits,
...         include_frame=ax is None,
...         ax=ax,
...         s=1,
...         label=f'y={y:0.2f}')
>>> _ = ax.legend()
>>> import matplotlib.pyplot as plt
>>> plt.show()
``````

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