Quantum Shor's Algorithm

Inspiration

The inspiration for this project came from the rapidly advancing field of quantum computing and its implications for cybersecurity. Shor’s algorithm, which has the potential to break widely used encryption like RSA, represents both an exciting breakthrough and a serious challenge for digital security. We wanted to explore its implementation, understand the current limitations, and evaluate its potential impacts, especially in the context of protecting critical urban infrastructure.

What it does

Our project implements Shor's algorithm, a quantum algorithm that factors large integers, which forms the basis of many encryption schemes. By demonstrating how Shor's algorithm can factorize numbers, we illustrate how quantum computing could eventually break traditional encryption, highlighting the need for quantum-safe security solutions.

How we built it

We built this project by programming using Qiskit library on python to Shor's algorithm on a quantum simulator, working within the constraints of noise and error that are typical in quantum computations. Our setup involved running the algorithm on increasingly large values of N, observing how quantum errors affected the accuracy of the factorization results as the problem size grew.

Challenges we ran into

Implementing Shor's algorithm posed several challenges. Quantum error rates significantly impacted our results, with the accuracy decreasing as N increased. Managing coherence time, error correction, and finding stable circuit configurations were also hurdles. Additionally, understanding the theoretical and practical aspects of Shor’s algorithm required deep dives into quantum mechanics and linear algebra.

Accomplishments that we're proud of

We are proud of successfully implementing Shor's algorithm to accurately factorize small numbers, despite high error rates. Our project showcases the practical limitations of current quantum hardware while still achieving meaningful results. It’s a valuable proof of concept for understanding quantum vulnerabilities in encryption and identifying areas for improvement.

What we learned

This project taught us about the practical challenges of quantum computing, including error management, coherence times, and the importance of optimized algorithms. We also learned how Shor’s algorithm could impact cybersecurity, highlighting the urgency of developing quantum-resistant encryption methods to protect sensitive information.

What's next for Quantum Shor's Algorithm

Next, we plan to focus on improving the algorithm’s reliability on quantum hardware by enhancing error correction techniques and refining our circuit design. Our results demonstrate the growing need for robust quantum error management to achieve accurate factorization on larger numbers. Additionally, we aim to explore quantum-resistant encryption methods and engage stakeholders on the importance of preparing for quantum cybersecurity challenges.

Built With

• css
• html
• javascript
• python
• qiskit