Applied Quantum Computing- Algorithms, Routing, and Error Correction

An end-to-end showcase of quantum computing implementations, spanning fundamental circuit design, cryptographic protocols, hardware-aware qubit routing, and advanced error correction.

Shor's Algorithm

Overview

This project is a culmination of multiple mini-projects focusing on quantum circuit design, cryptography, algorithm analysis, device routing, and error correction. It showcases the complete, from-scratch implementation of fundamental and advanced quantum computing concepts:-

1. Quantum Fundamentals & Cryptography

Engineered essential quantum circuits to demonstrate superposition and entanglement. Developed a fully functional Quantum Adder with logical operations for Quantum AND, OR, XOR, and Signed Addition. Implemented the BB84 Protocol for secure quantum information transmission, successfully incorporating mechanisms to detect eavesdropper (Eve) presence.

2. Quantum Algorithm Analysis

Implemented and analyzed core algorithms, including Deutsch and Deutsch-Jozsa algorithms for evaluating constant and balanced functions, and Simon’s Algorithm for period finding. Developed a Grover’s Algorithm circuit utilizing phase rotation and inversion oracles to amplify and find target states. Built both ideal and noisy Bernstein-Vazirani circuits to study the impact of hardware control errors. Realized Superdense Coding to transmit classical binary information over quantum channels.

3. Qubit Allocation and Routing

Explored the constraints of physical quantum hardware by decomposing benchmark circuits into distinct basis gate sets. Applied the SABRE algorithm to map these circuits onto various device topologies (such as Grid and Ring layouts), optimizing for average circuit depth and minimizing SWAP insertions. Simulated a NISQ (Noisy Intermediate-Scale Quantum) machine by constructing custom noisy CNOT gates and formulated optimal logical-to-physical qubit mapping to maximize overall circuit fidelity on 4-qubit and 5-qubit topologies.

4. Quantum Error Correction & QAOA

Designed robust encoder and decoder circuits to implement both bit-flip and phase-flip Quantum Error Correction (QEC), successfully recovering initial states after single or double error injections. Finally, engineered a Quantum Approximate Optimization Algorithm (QAOA) solver to evaluate node partitions and efficiently solve the Max-Cut problem on simple, undirected graphs.