Add demo "How to Quantum Just-In-Time Compile Grover's Algorithm with Catalyst" (#1219)

**Title:** How to Quantum Just-In-Time Compile Grover's Algorithm with
Catalyst

**Summary:** This demo uses the existing [Grover's
Algorithm](https://pennylane.ai/qml/demos/tutorial_grovers_algorithm/)
tutorial to describe how to just-in-time (JIT) compile a quantum circuit
using Catalyst. It also includes runtime benchmarks to demonstrate the
performance improvements that JIT compiling with Catalyst offers.

**Relevant references:** [L. K. Grover (1996) "A fast quantum mechanical
algorithm for database
search"](https://dl.acm.org/doi/10.1145/237814.237866)

**Possible Drawbacks:** None

**Related GitHub Issues:** None


[[sc-72939](https://app.shortcut.com/xanaduai/story/72939/convert-another-selected-demo)]

----
If you are writing a demonstration, please answer these questions to
facilitate the marketing process.

* GOALS — Why are we working on this now?

* Promote Catalyst by demonstrating the performance improvements it
offers by QJIT compiling a relatively simple quantum circuit.


* AUDIENCE — Who is this for?

* Users of PennyLane looking to compile and optimize their circuits for
better performance.


* KEYWORDS — What words should be included in the marketing post?

  * Grover's algorithm
  * Catalyst
  * QJIT

* Which of the following types of documentation is most similar to your
file?
(more details
[here](https://www.notion.so/xanaduai/Different-kinds-of-documentation-69200645fe59442991c71f9e7d8a77f8))
    
- [ ] Tutorial
- [ ] Demo
- [x] How-to

---------

Co-authored-by: Josh Izaac <josh146@gmail.com>
Co-authored-by: Ivana Kurečić <ivana@xanadu.ai>

Author: 3 people

_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_qjit_compile_grovers_algorithm_with_catalyst.png

@@ -0,0 +1,64 @@
+{
+    "title": "How to quantum just-in-time (QJIT) compile Grover's algorithm with Catalyst",
+    "authors": [
+        {
+            "username": "joeycarter"
+        }
+    ],
+    "dateOfPublication": "2024-11-07T00:00:00+00:00",
+    "dateOfLastModification": "2024-11-07T00:00:00+00:00",
+    "categories": [
+        "Algorithms",
+        "Devices and Performance",
+        "How-to",
+        "Quantum Computing"
+    ],
+    "tags": [],
+    "previewImages": [
+        {
+            "type": "thumbnail",
+            "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_qjit_compile_grovers_algorithm_with_catalyst.png"
+        },
+        {
+            "type": "large_thumbnail",
+            "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_qjit_compile_grovers_algorithm_with_catalyst.png"
+        }
+    ],
+    "seoDescription": "See how to use Catalyst to just-in-time (QJIT) compile a PennyLane circuit implementing Grover's algorithm.",
+    "doi": "",
+    "references": [
+        {
+            "id": "Grover1996",
+            "type": "article",
+            "title": "A fast quantum mechanical algorithm for database search",
+            "authors": "L. K. Grover",
+            "year": "1996",
+            "journal": "Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing",
+            "doi": "10.1145/237814.237866"
+        },
+        {
+            "id": "NandC2000",
+            "type": "book",
+            "title": "Quantum Computation and Quantum Information",
+            "authors": "M. A. Nielsen, and I. L. Chuang",
+            "year": "2000",
+            "publisher": "Cambridge University Press",
+            "journal": "",
+            "url": ""
+        }
+    ],
+    "basedOnPapers": [],
+    "referencedByPapers": [],
+    "relatedContent": [
+        {
+            "type": "demonstration",
+            "id": "tutorial_grovers_algorithm",
+            "weight": 1.0
+        },
+        {
+            "type": "demonstration",
+            "id": "tutorial_how_to_quantum_just_in_time_compile_vqe_catalyst",
+            "weight": 1.0
+        }
+    ]
+}