Teaching Quantum Computing Via Hands-on Circuit Simulation Deepens Graduate Students’ Understanding of Fundamental Computing Concepts

Quantum computing represents a paradigm shift in computation, yet translating its theoretical promise into practical expertise requires innovative educational approaches. Florian Krötz, Xiao-Ting Michelle To, and Korbinian Staudacher, alongside Dieter Kranzlmüller from Ludwig-Maximilians-Universität München, addressed this challenge by designing a hands-on practical course for graduate computer science students. The team developed a curriculum centred around implementing quantum circuit simulators, allowing students to directly engage with core concepts such as superposition and the impact of noise. This immersive approach moves beyond abstract theory, fostering a deeper understanding of quantum computation and equipping the next generation of researchers with the practical skills needed to advance the field. The work details their teaching methodology, course structure, and valuable insights gained from student evaluations, offering a blueprint for effective quantum computing education.

The curriculum focuses on equipping students with a deep understanding of core concepts without requiring extensive prior knowledge. A key component of the course involves exploring tensor networks, a powerful technique for simulating complex quantum systems. This approach bridges the gap between theoretical concepts and practical realization, allowing students to understand how quantum algorithms function in practice. The course also incorporates benchmarking and validation techniques, encouraging students to evaluate the performance of different quantum simulators.

The course is designed for students with a background in linear algebra and some programming experience, making quantum computing accessible to those new to the field. The curriculum includes foundational concepts like quantum states and circuits, simulation techniques such as tensor networks and stabilizer decompositions, and software tools like NumPy, Qiskit, and Cirq. Students may also gain experience with cloud-based quantum computers through IBM Quantum. The course is often delivered in intensive workshop or school settings, providing a focused learning environment. A strong foundation in linear algebra is considered essential, and resources like MIT OpenCourseware and lectures by Gilbert Strang are recommended.

Students explore qubits, quantum circuits, stabilizer decompositions, and tensor networks, learning to represent and manipulate high-dimensional quantum states. They utilize software tools like NumPy for numerical computation, Qiskit and Cirq for quantum computing frameworks, and OpenQASM, a quantum assembly language. The course highlights tensor networks as a key technique for simulating quantum systems, particularly those challenging for traditional methods, and utilizes stabilizer circuits for efficient simulation. The work provides links to valuable resources, including IBM Quantum Learning and Experience, Cirq documentation, and information about workshops and schools on tensor methods and networks. Online courses and lectures on linear algebra are also recommended, alongside research papers on quantum supremacy and simulation techniques. Overall, this work represents a comprehensive overview of a modern approach to teaching quantum computing, emphasizing hands-on learning, practical implementation, and the use of powerful simulation techniques like tensor networks.

Quantum Simulators Enhance Graduate Understanding

This work details a practical course designed to deepen graduate students’ understanding of quantum computing through hands-on implementation of circuit simulators. Students explore fundamental concepts by building simulators based on state vectors, density matrices, the stabilizer formalism, and matrix product states, gaining practical experience alongside theoretical knowledge. The state vector simulation component requires students to validate their implementation by generating Bell and GHZ states, visually confirming the representation of quantum states. Measurements are then implemented using operators, demonstrating how these operators act on the state vector and require normalization to maintain probabilistic consistency.

The density matrix simulator builds upon this foundation, allowing students to model quantum states and apply gates, while also introducing various error types, including bit flip, phase flip, bit phase flip, depolarization, and amplitude damping. The stabilizer formalism is explored through a pen-and-paper exercise, utilizing a tableau representation to efficiently encode quantum states and Clifford gates, demonstrating how the Hadamard gate operates within this framework. Students represent states using Pauli strings and efficiently apply gates through bit operations on the tableau, gaining a deeper understanding of the underlying principles. The final simulator implemented before the project focuses on matrix product states, a technique for representing quantum states with reduced computational complexity.

Students learn tensor notation and contraction, applying these concepts to represent qubits as tensors and apply single and two-qubit gates. Through a detailed example involving the CNOT gate and singular value decomposition, students observe how entanglement impacts tensor size, demonstrating the efficiency of MPS for representing unentangled states. This culminates in a student project, building upon the skills developed throughout the course.

Building Quantum Simulators Deepens Student Understanding

This work details the development and evaluation of a practical course designed to deepen graduate students’ understanding of quantum computing fundamentals. The course moves beyond simply using existing quantum simulators, instead challenging students to implement several key simulation methods themselves, including state vector, density matrix, stabilizer formalism, and matrix product states techniques. Through this hands-on approach, students gain a more thorough grasp of core concepts like superposition and the effects of noise, preparing them for advanced research in the field. The evaluation of this course demonstrates that building simulators from scratch effectively reinforces fundamental knowledge and allows students to critically assess the strengths and weaknesses of different simulation methods. While acknowledging that students may enter the course with varying levels of prior knowledge regarding tensor networks, the curriculum successfully introduces these concepts and equips students with the tools to understand related research literature. Future work may focus on expanding the course to incorporate more advanced topics and further refine the learning experience based on ongoing evaluation and student feedback.