Classical Implementation & Testing of Shor’s Algorithm (#12318)

[adityakrmishra]

Hi everyone!

I have worked on implementing and testing a classical simulation of Shor’s Algorithm without using quantum computing libraries like Qiskit or Cirq. The goal is to demonstrate how Shor’s Algorithm factors composite numbers in a classical setting.

✅ Implementation Highlights:

• Uses modular exponentiation and order-finding to determine factors.
• Checks for trivial factors before proceeding with the order-finding method.
• Returns valid non-trivial factors of N.

✅ Added Tests:

• Unit tests cover multiple values of N (e.g., 15, 21, 35, 55).
• Ensures correctness using pytest.

💡 Discussion Points:

• Are there ways to optimize the order-finding process?
• Should we add support for larger numbers?
• Any edge cases we should test?

📌 You can find the PR here: PR #12545
Let me know your thoughts and feedback! 🚀

Thanks!