Demo about implementing Shor's algorithm with Catalyst (#1010)

**Title:** JIT compiling Shor's algorithm with PennyLane and Catalyst

**Summary:** Over the past year, PennyLane has been integrated with
Catalyst, allowing for quantum just-in-time compilation of classical and
quantum code together. This demo leverages that integration to implement
a version of Shor's factoring algorithm that is just-in-time compiled
from end-to-end, classical control structure and all.

**Relevant references:** See within

**Possible Drawbacks:** As it stands, it's quite long (especially for
the amount of actual output); I am not sure about the ending.

**Related GitHub Issues:** N/A

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

* GOALS — Why are we working on this now?

Highlight PennyLane and Catalyst integration, and expose challenges (and
opportunities) in scaling up quantum compilation pipelines.

* AUDIENCE — Who is this for?

Primarily people researchers and developers focused on quantum
compilation.


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

quantum compilation; quantum circuits; quantum algorithms; Shor's
algorithm

* 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
- [X] Demo
- [ ] How-to


[sc-75726]

---------

Co-authored-by: Olivia Di Matteo <[email protected]>
Co-authored-by: Josh Izaac <[email protected]>
Co-authored-by: David Ittah <[email protected]>
Co-authored-by: justinpickering <[email protected]>
Co-authored-by: Justin Pickering <[email protected]>
Co-authored-by: Alvaro Ballon <[email protected]>

Author: 6 people

_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_shor_algorithm_catalyst_pennylane.png

@@ -0,0 +1,98 @@
+{
+    "title": "Quantum just-in-time compiling Shor's algorithm with Catalyst",
+    "authors": [
+        {
+            "username": "glassnotes"
+        }
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+    "dateOfPublication": "2025-04-04T09:00:00+00:00",
+    "dateOfLastModification": "2025-04-04T09:00:00+00:00",
+    "categories": [
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+        "Quantum Computing",
+        "Devices and Performance"
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+    "tags": [],
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+    "seoDescription": "Just-in-time compile Shor's algorithm from end-to-end with PennyLane and Catalyst.",
+    "doi": "",
+    "references": [
+        {
+            "id": "Shor1997",
+            "type": "article",
+            "title": "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer",
+            "authors": "Peter W. Shor",
+            "year": "1997",
+            "journal": "SIAM Journal on Computing Vol. 26, Iss. 5",
+            "doi": "10.1137/S0097539795293172",
+            "url": "https://doi.org/10.1137/S0097539795293172"
+        },
+        {
+            "id": "PurpleDragonBook",
+            "type": "book",
+            "title": "Compilers: Principles, Techniques, And Tools",
+            "authors": "Alfred V Aho, Monica S Lam, Ravi Sethi, Jeffrey D Ullman",
+            "year": "2007",
+            "publisher": "Pearson",
+            "url": "https://www.pearson.com/en-us/subject-catalog/p/compilers-principles-techniques-and-tools/P200000003472/9780133002140"
+        },
+        {
+            "id": "JAXJIT",
+            "type": "webpage",
+            "title": "Just-in-time compilation",
+            "authors": "The JAX Authors",
+            "year": "2024",
+            "publisher": "",
+            "url": "https://docs.jax.dev/en/latest/jit-compilation.html"
+        },
+        {
+            "id": "Beauregard2003",
+            "type": "article",
+            "title": "Circuit for Shor's algorithm using 2n+3 qubits",
+            "authors": "Stephane Beauregard",
+            "year": "2003",
+            "journal": "Quantum Info. Comput.",
+            "doi": "10.5555/2011517.2011525",
+            "url": "https://dl.acm.org/doi/10.5555/2011517.2011525"
+        },
+        {
+            "id": "Draper2000",
+            "type": "preprint",
+            "title": "Addition on a Quantum Computer",
+            "authors": "Thomas G. Draper",
+            "year": "2000",
+            "journal": "",
+            "doi": "10.48550/arXiv.quant-ph/0008033",
+            "url": "https://doi.org/10.48550/arXiv.quant-ph/0008033"
+        }
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+}