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Tutorials for lab_dev and physics #392

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Tutorials for lab_dev and physics #392

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Context: Visualize the docs from this PR.

Description of the Change:

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Another general comment, some of this can be confusing if one has no idea of the concept of wires (potential 4 wires, in/out + bra/ket). Before a talk from Fillipo last week I had never heard about this idea before. Maybe it would be nice with a general intro or maybe a link to the wires channel that introduces this important concept that is used throughout (unless it is obvious to anyone in the CV community).

@sylviemonet sylviemonet removed the WIP work in progress label May 15, 2024
@sylviemonet sylviemonet changed the title Tutorials [DO NOT MERGE] Tutorials for lab_dev and physics May 15, 2024
:no-heading:
:include-all-objects:

This section of functions is the helper function section to calculate properties of object in Fock representation, which needs to be rearranged and possibly be moved under Fock representation class.
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Suggested change
This section of functions is the helper function section to calculate properties of object in Fock representation, which needs to be rearranged and possibly be moved under Fock representation class.
This module contains helper functions to calculate properties of objects in Fock representation.

This module contains the classes for the available ansatze.

Ansatze are supposed to store the data related to the Representation and support basic mathematical operations.
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Suggested change
Ansatze are supposed to store the data related to the Representation and support basic mathematical operations.
Ansatze store the data related to the Representation and support basic mathematical operations.


The wires in the diagram below correspond to the `out_ket` wires (:math:`\alpha^*`) and the `in_ket` wires (:math:`\beta`) in :class:`~mrmustard.lab_dev.wires.Wires`.

As for a ``n``-mode Gaussian Channel :math:`\langle \vec{\alpha}|\Psi(|\vec{\gamma}\rangle\langle\vec{\delta}|)|\vec{\beta}`, the variable vector denotes :math:`\vec{\alpha} = (\alpha^*_0, \alpha^*_1, ..., \alpha^*_{n-1}, \beta_0, \beta_1,..., \beta_{n-1}, \delta^*_0, \delta^*_1, ..., \delta^*_{n-1}, \gamma_0, \gamma_1,..., \gamma_{n-1})`.
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for channels the default order is out,in,out,in so alpha, delta, beta, gamma in your notation

║ |psi> ║─────▶ alpha^*_0 alpha_0─────▶║ U ║─────▶ beta^*_0
╚═══════╝ ╚═════╝
|
| integral on alpha
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I don't understand what is the vertical line is for?

║ |psi> ║─────▶ alpha^*_0 alpha^*_0─────▶║ ║─────▶ beta^*_0
╚═══════╝ ╚═══════╝
|
| Add the ajoint part
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if you mean this is "equality" or "follows", it's very confusing to me because it looks like a wire

.. code-block::

╔═══════╗ ╔═══════╗
║ |psi> ║─────▶ ║ DsMap ║─────▶
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this is a bit confusing because DsMap has ket and bra input

.. code-block::

╔═══════╗ ╔══════════════╗
║ |psi> ║─────▶ ║ BtoQMap.dual ║─────▶
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are you sure? wouldn't this call the complex integral at the moment?

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