# cirq.scatter_plot_normalized_kak_interaction_coefficients¶

cirq.scatter_plot_normalized_kak_interaction_coefficients(interactions: Iterable[Union[numpy.ndarray, cirq.SupportsUnitary, KakDecomposition]], *, include_frame: bool = True, ax: Optional[matplotlib.axes._axes.Axes] = None, **kwargs)[source]

Plots the interaction coefficients of many two-qubit operations.

Plots:
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)

Parameters
• 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

Returns

The matplotlib 3d axes object that was plotted into.

Examples

>>> 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()