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

[joeycarter]

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

Summary: This demo uses the existing Grover's 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"

Possible Drawbacks: None

Related GitHub Issues: None

[sc-72939]

---

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)

• [ ] Tutorial
• [ ] Demo
• [x] How-to