# cirq.linalg.scatter_plot_normalized_kak_interaction_coefficients

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)

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.

#### 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()
[{ "type": "thumb-down", "id": "missingTheInformationINeed", "label":"Missing the information I need" },{ "type": "thumb-down", "id": "tooComplicatedTooManySteps", "label":"Too complicated / too many steps" },{ "type": "thumb-down", "id": "outOfDate", "label":"Out of date" },{ "type": "thumb-down", "id": "samplesCodeIssue", "label":"Samples / code issue" },{ "type": "thumb-down", "id": "otherDown", "label":"Other" }]
[{ "type": "thumb-up", "id": "easyToUnderstand", "label":"Easy to understand" },{ "type": "thumb-up", "id": "solvedMyProblem", "label":"Solved my problem" },{ "type": "thumb-up", "id": "otherUp", "label":"Other" }]