Quantum Permutation Synchronization

Overview

This project is based on the research paper Quantum Permutation Synchronization. It explores the application of quantum computing techniques — specifically QUBO formulation and QAOA — to the problem of permutation synchronization.

Permutation synchronization is a fundamental problem in computer vision and network analysis, where the goal is to find consistent mappings between different sets of objects. The project demonstrates how quantum algorithms can be applied to these complex combinatorial optimization problems.

Implementation

The project implements both classical and quantum approaches to permutation synchronization, enabling direct comparison of results. The quantum implementation uses QAOA circuits and quantum annealing.

• QUBO formulation of the permutation synchronization problem
• QAOA circuit implementation using Qiskit
• Quantum annealing solver integration
• Performance comparison and visualization tools
• Point matching algorithms for computer vision applications

Results

Point matching across images was accomplished using both QAOA and quantum annealing. The same QUBO formulation was solved with both methods, and the results were compared in terms of solution quality and computational efficiency.