Bridging Theory and Practice: Teaching Quantum Algorithms Through MATLAB

In the last year, quantum computing has rapidly transitioned from a purely theoretical field into applied engineering, where multiple algorithms can approach combinatorial optimization problems, machine learning, and cryptography in novel ways, often achieving speedup compared to classical solutions. In this context, there is an increasing need for educational tools that connect mathematical principles from quantum information theory with practical experimentation. Yet, most existing educational resources remain either highly theoretical or provide fragmented code examples, with limited analysis and applications to real-world use cases. As a result, students’ experiences appear restricted, with non-interactive tools for learning. This work presents a comprehensive framework for teaching quantum computing through interactive resources, developed via MATLAB Live Scripts. By combining theory, executable code, and visualization tools within a single environment, this framework enhances learners’ ability to see and reason about quantum algorithms step by step. Following the principles of Project-Based Learning in STEM education, we present a diverse collection of quantum resources, including algorithms for optimization, communication, and error correction. Each project operates as a self-contained learning unit, offering modularity, white-box implementations, and tools for visualization and analysis. Beyond its educational impact, this framework also employs and extends the MATLAB Support Package for Quantum Computing, offering an open-source, reproducible environment suitable for courses and independent study.