# An example Jupyter Notebook#

This notebook is a demonstration of directly-parsing Jupyter Notebooks into Sphinx using the MyST parser.[^download]

## Markdown#

### Configuration#

To build documentation from this notebook, the following options are set:

myst_enable_extensions = [
"amsmath",
"colon_fence",
"deflist",
"dollarmath",
"html_image",
]
myst_url_schemes = ("http", "https", "mailto")


### Syntax#

As you can see, markdown is parsed as expected. Embedding images should work as expected. For example, here’s the MyST-NB logo:

![myst-nb logo](../img/unitary_fund_logo.png) By adding "html_image" to the myst_enable_extensions list in the sphinx configuration (see here), you can even add HTML img tags with attributes:

<img src="../img/unitary_fund_logo.png" alt="logo" width="200px" class="shadow mb-2"> Because MyST-NB is using the MyST-markdown parser, you can include rich markdown with Sphinx in your notebook. For example, here’s a note admonition block:

Note

Wow, a note! It was generated with this code (as explained here):

:::{note}
**Wow**, a note!
:::


If you wish to use “bare” LaTeX equations, then you should add "amsmath" to the myst_enable_extensions list in the sphinx configuration. This is explained here, and works as such:

\begin{equation}
\frac {\partial u}{\partial x} + \frac{\partial v}{\partial y} = - \, \frac{\partial w}{\partial z}
\end{equation}

\begin{align*}
2x - 5y &=  8 \\
3x + 9y &=  -12
\end{align*}

(1)#$\begin{equation} \frac {\partial u}{\partial x} + \frac{\partial v}{\partial y} = - \, \frac{\partial w}{\partial z} \end{equation}$
\begin{align*} 2x - 5y &= 8 \\ 3x + 9y &= -12 \end{align*}

Also you can use features like equation numbering and referencing in the notebooks:

$$e^{i\pi} + 1 = 0$$ (euler)

(2)#$e^{i\pi} + 1 = 0$

Euler’s identity, equation (2), was elected one of the most beautiful mathematical formulas.

You can see the syntax used for this example here in the MyST documentation.

## Code cells and outputs#

You can run cells, and the cell outputs will be captured and inserted into the resulting Sphinx site.

### __repr__ and HTML outputs#

For example, here’s some simple Python:

import matplotlib.pyplot as plt
import numpy as np
data = np.random.rand(3, 100) * 100
data[:, :10]

array([[41.70666377, 26.22816363, 86.3986639 ,  1.3731835 , 14.10975912,
40.81947407, 70.66855368, 36.70683473, 77.84341938,  3.396122  ],
[57.60765977, 28.88031167,  0.22750555, 70.57419678, 31.17699799,
94.86070417,  3.9733227 , 87.05020935,  4.93405144, 15.05767401],
[55.88455176, 54.72249918,  1.34378086, 88.70779508, 47.81738406,
96.26981048, 47.76120301, 53.00534583, 20.83838575, 40.0995143 ]])


This will also work with HTML outputs

import pandas as pd
df = pd.DataFrame(data.T, columns=['a', 'b', 'c'])

a b c
0 41.706664 57.607660 55.884552
1 26.228164 28.880312 54.722499
2 86.398664 0.227506 1.343781
3 1.373183 70.574197 88.707795
4 14.109759 31.176998 47.817384

as well as math outputs

from IPython.display import Math
Math(r"\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}")

$\displaystyle \sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$

This works for error messages as well:

print("This will be properly printed...")
print(thiswont)

This will be properly printed...

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In , line 2
1 print("This will be properly printed...")
----> 2 print(thiswont)

NameError: name 'thiswont' is not defined


### Images#

Images that are generated from your code (e.g., with Matplotlib) will also be embedded.

fig, ax = plt.subplots()
ax.scatter(*data, c=data)

<matplotlib.collections.PathCollection at 0x7fb028ec1af0> ### Testing#

The following cells setup a test (which won’t be rendered in the notebook), the test code and the test output cell:

SIMULATOR = DensityMatrixSimulator()
# 0.1% depolarizing noise
qbit = LineQubit(0)
circ = Circuit(X(qbit) for _ in range(80))

def simulate_with_noise(circ: Circuit) -> float:
circuit = circ.with_noise(depolarize(p=0.001))
rho = SIMULATOR.simulate(circuit).final_density_matrix
# define the computational basis observable
obs = np.diag([1, 0])
expectation = np.real(np.trace(rho @ obs))
return expectation

unmitigated = simulate_with_noise(circ)
exact = 1
print(f"Error in simulation is {exact - unmitigated:.{3}}")

Error in simulation is 0.0506