Initial state preparation demo (#950)

**Title:**

Initial state preparation for quantum chemistry

**Summary:**

This demo is explaining the concept of an initial state -- a primer for
a quantum algorithm that improves its chances of success specifically
for the task of obtaining the ground-state energy of a molecule. It
showcases the newly built functionality in PennyLane for importing
outputs from sophisticated computational chemistry methods to initialize
better initial states. Finally, it shows how the choice of initial state
affects the execution of VQE on a simple molecule, demonstrating the
importance of initial state for quantum algorithms and that this can of
algorithms R&D can be now performed in PennyLane.

**Relevant references:**

**Possible Drawbacks:**

**Related GitHub Issues:**

---------

Co-authored-by: soranjh <[email protected]>
Co-authored-by: soranjh <[email protected]>
Co-authored-by: Alvaro Ballon <[email protected]>
Co-authored-by: Guillermo Alonso-Linaje <[email protected]>

_static/authors/stepan_fomichev.txt

@@ -0,0 +1,5 @@
+.. bio:: Stepan Fomichev
+   :photo: ../_static/authors/stepan_fomichev.jpg
+
+
+   Stepan Fomichev is a quantum scientist working at Xanadu. His background is in condensed matter physics, with a focus on lattice vibrations and electron-phonon coupling. As part of the Algorithms team, he focuses on researching and developing prospective applications for quantum algorithms.

demonstrations/tutorial_initial_state_preparation.metadata.json

@@ -0,0 +1,43 @@
+{
+    "title": "Initial State Preparation for Quantum Chemistry",
+    "authors": [
+        {
+            "id": "stepan_fomichev"
+        }
+    ],
+    "dateOfPublication": "2023-10-20T00:00:00+00:00",
+    "dateOfLastModification": "2023-10-20T00:00:00+00:00",
+    "categories": [
+        "Quantum Chemistry"
+    ],
+    "tags": [],
+    "previewImages": [
+        {
+            "type": "thumbnail",
+            "uri": "/_images/thumbnail_initial_state_preparation.png"
+        },
+        {
+            "type": "large_thumbnail",
+            "uri": "/_static/large_demo_thumbnails/thumbnail_large_initial_state_preparation.png"
+        }
+    ],
+    "seoDescription": "Prepare initial states for quantum algorithms from output of traditional quantum chemistry methods.",
+    "doi": "",
+    "canonicalURL": "/qml/demos/tutorial_initial_state_preparation",
+    "references": [
+    ],
+    "basedOnPapers": [],
+    "referencedByPapers": [],
+    "relatedContent": [
+        {
+            "type": "demonstration",
+            "id": "tutorial_quantum_chemistry",
+            "weight": 1.0
+        },
+        {
+            "type": "demonstration",
+            "id": "tutorial_vqe",
+            "weight": 1.0
+        }
+    ]
+}

demos_quantum-chemistry.rst

@@ -105,6 +105,12 @@ Quantum chemistry is one of the leading application areas of quantum computers.
     :description: :doc:`demos/tutorial_fermionic_operators`
     :tags: chemistry
 
+.. gallery-item::
+    :tooltip: Initial State Preparation for Quantum Chemistry
+    :figure: demonstrations/initial_state_preparation/thumbnail_initial_state_preparation.png
+    :description: :doc:`demos/tutorial_initial_state_preparation`
+    :tags: chemistry
+
 :html:`</div></div><div style='clear:both'>`
 
 
@@ -127,4 +133,5 @@ Quantum chemistry is one of the leading application areas of quantum computers.
     demos/tutorial_classically_boosted_vqe
     demos/tutorial_qchem_external
     demos/tutorial_resource_estimation
+    demos/tutorial_initial_state_preparation