Mathematical Foundations of Quantum Computing

A set of fundamental mathematical tools for Quantum Computing

What you'll learn
Linear Algebra
Qubits
Inner Product
Linear Operators
Commutation
Unitary Matrices
Hermitian Matrices
Eigenvalues and Eigenvectors
Tensor Product
Entanglement
Postulates of Quantum Theory
Quantum Circuits
Teleportation Protocol

Requirements
Familiarity with high school-level mathematics (functions, matrices, probability, vectors, geometry, trigonometry, and complex numbers)
Mathematical curiosity!

Description
Master the mathematical tools behind quantum computing and build a solid foundation for understanding quantum algorithms and quantum information theory.This course explores the fundamental mathematical concepts behind quantum computing, with a strong focus on their relevance to quantum physics. It starts with formal definitions and simple examples to build intuition, then revisits key topics while adding new layers of information - ensuring a clear and structured learning path. You will develop a deep understanding of the mathematical foundations of quantum computing, particularly through the lens of linear algebra tailored to quantum systems. I provide detailed proofs of important properties and explain the core ideas in an intuitive way to give you deeper insights and future problem-solving skills.What makes this course unique:Strong focus on the mathematical theory behind quantum computingFormal definitions motivated by their relevance in quantum computing and explained through several examplesStep-by-step solutions to exercises proposed during the lecturesMore than 60 conceptual multiple-choice questions across 11 quizzes for knowledge reinforcementLearning Strategy:This course can feel dense depending on your background, but a helpful strategy is to focus on the examples. Understanding concrete examples is key to grasping the meaning of abstract concepts. You’re encouraged to pause the lectures, review the calculations, work through the examples, and then return to the more abstract material. Taking time to reflect and using a back-and-forth approach will help you build both knowledge and intuition.Once you’ve mastered these concepts, navigating the field of quantum computing will become much smoother. My goal is to equip you with a solid understanding of the mathematical techniques widely used in quantum theory and quantum computing.

Who this course is for
Beginner: Anyone curious about the mathematical background of quantum computing!
Advanced: Students, programmers, and engineers interested in deepening their understanding of quantum computing!