Quantum Factoring with Shor's Algorithm

This project implements Shor's algorithm to factor the number 77 using IBM Quantum's cloud service.

Prerequisites

• Python 3.9 or higher
• pip (Python package installer)
• IBM Quantum account

Installation

1. Create and activate a virtual environment (recommended):

python -m venv skibbidi
source skibbidi/bin/activate  

2. Install required packages:

pip install qiskit[all]~=1.3.1
pip install qiskit-ibm-runtime~=0.34.0

IBM Quantum Setup

1. Create an IBM Quantum account at https://quantum.ibm.com/
2. Log in and get your API token from your account settings
3. Replace YOUR_API_TOKEN in the code with your actual token

Running the Program

1. Run the program:

python diddy.py

The program will:

• Connect to IBM Quantum
• Submit the quantum circuit to the ibm_brisbane backend
• Monitor job execution
• Display results when complete

Example Output

A successful run will show:

Running on ibm_brisbane
Job ID: [job_id]
Current status: QUEUED
...
Current status: RUNNING
...
Job completed, processing results...

Processed 5000 shots
Top 10 most frequent measurements:
[measurement details]

All factors found: [7, 11]

Understanding the Results

The program attempts to factor N=77 using Shor's algorithm. A successful run will find the factors 7 and 11. The output shows:

• Quantum measurements and their frequencies
• Period calculations for each measurement
• Factors found from the period calculations
• Overall statistics about the quantum measurements

Troubleshooting

• If the job times out, you can retrieve results later using the job ID
• Check the IBM Quantum dashboard to monitor job status
• Ensure your API token is valid and has not expired

Notes

• Quantum computing time is limited for free accounts
• Jobs may queue depending on backend availability
• Results are probabilistic due to the quantum nature of the algorithm