Merge branch 'docs-v2' of https://github.com/pasqal-io/Pulser into ac…

…/docs_hw

docs/source/conf.py

@@ -40,6 +40,7 @@
     "sphinx.ext.autodoc",
     "sphinx.ext.mathjax",
     "sphinx.ext.napoleon",
+    "sphinx.ext.autosummary",
     "sphinx_autodoc_typehints",
 ]
 

docs/source/conventions.md

@@ -122,6 +122,11 @@ sample
 
 ## Hamiltonians
 
+:::{tip}
+This section uses formulas that rely on the [Indexed Operator](#indexed-operator)
+notation.
+:::
+
 Independently of the mode of operation, the Hamiltonian describing the system
 can be written as
 
@@ -258,3 +263,21 @@ $$
 :::{note}
 The definitions given for both interaction Hamiltonians are independent of the chosen state vector convention.
 :::
+
+## Notation
+
+### Indexed Operator
+
+Whenever an arbitrary operator is written with an index (typically $i$ or $j$), e.g. $\hat{O}_i$, it is implicit that $\hat{O}$ is applied *only* to qudit $i$ while the rest of the qudits are applied the identity operator, $\hat{I}$. Put another way,
+
+$$ \hat{O}_i = \underset{(1)}{\hat{I}} \otimes \underset{(2)}{\hat{I}} \otimes ... \otimes\ \underset{(i)}{\hat{O}}\ \otimes ... \otimes \underset{(N)}{\hat{I}},$$
+
+where $1 \leq i \leq N$.
+
+This notation is extendable to multiple indices. Take for instance the case with two indices, $\hat{O}_{ij}$ – here, $\hat{O}$ is a two-qudit operator. A good example is the [interaction Hamiltonian](#interaction-hamiltonian) in the `ground-rydberg` basis, which we write as
+
+$$H^\text{int}_{ij} = \frac{C_6}{R_{ij}^6} \hat{n}_i \hat{n}_j = \frac{C_6}{R_{ij}^6} \left( \underset{(1)}{\hat{I}} \otimes ... \otimes \ \underset{(j)}{\hat{n}}\ \otimes ... \otimes \ \underset{(i)}{\hat{n}} \ \otimes ... \otimes \underset{(N)}{\hat{I}}\right),$$
+
+where $1 \leq j < i \leq N$.
+
+Note that, generally, we cannot write $\hat{O}_{ij}$ in the form used above because $\hat{O}$ might not be separable in a tensor product of two single-qudit operators, but the operator is valid nonetheless.

docs/source/index.rst

@@ -46,23 +46,19 @@ of quantum programs written with Pulser on :doc:`tutorials/creating`.
 
 .. toctree::
    :maxdepth: 2
-   :caption: Installation and First Steps
+   :caption: Getting Started
 
    installation
    programming
    tutorials/creating
 
 .. toctree::
    :maxdepth: 2
-   :caption: Fundamental Concepts
+   :caption: Fundamentals
 
    conventions
+   register
    hardware
-
-.. toctree::
-   :maxdepth: 2
-   :caption: Backend Execution
-
    tutorials/backends
 
 .. toctree::
@@ -92,20 +88,11 @@ of quantum programs written with Pulser on :doc:`tutorials/creating`.
 
 .. toctree::
    :maxdepth: 1
-   :caption: Quantum Simulation
+   :caption: Quantum Simulation & Applications
 
    tutorials/afm_prep
    tutorials/optimization
    tutorials/xy_spin_chain
-   tutorials/mw_engineering
-   tutorials/shadow_est
-   tutorials/1D_crystals
-
-.. toctree::
-   :maxdepth: 1
-   :caption: Other Applications
-
-   tutorials/cz_gate
    tutorials/qubo
 
 .. toctree::

docs/source/programming.md

@@ -46,6 +46,10 @@ Here $H(t)$ is the Hamiltonian describing the evolution of the system. For a sys
 
 $$ \left|\Psi_f\right> = \exp\left(-\frac{i}{\hbar}\int_0^{\Delta t} H(t) dt\right)\left|\Psi_0\right>$$
 
+:::{tip}
+The equation below uses the [Indexed Operator](conventions.md#indexed-operator) notation.
+:::
+
 The Hamiltonian describing the evolution of the system can be written as
 
 $$
@@ -65,7 +69,7 @@ and $j$.
 The driving Hamiltonian describes the effect of a pulse on two energy levels of an individual atom, $|a\rangle$ and $|b\rangle$. A pulse is determined by its duration $\Delta t$, its Rabi frequency $\Omega(t)$, its detuning $\delta(t)$ and its phase $\phi$ (constant along the duration of the pulse). Between $0$ and $\Delta t$, the driving Hamiltonian is:
 
 $$
-H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-j\phi} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{j\phi} |b\rangle\langle a| - \delta(t) |b\rangle\langle b|
+H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-i\phi} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{i\phi} |b\rangle\langle a| - \delta(t) |b\rangle\langle b|
 $$
 
 <details>