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The Math Behind Quantum Computing

Learn the math behind quantum computing -- linear algebra, qubits, quantum logic gates, superposition, and entanglement explained visually. This beginner-friendly video visually explains core concepts from single qubits to principles for implementing algorithms on quantum computers. This video dives into the linear algebra of quantum computing. A foundation is built on the geometric interpretation of qubits as two-dimensional vectors, and the mathematical interpretation of quantum logic gates as matrices acting on these vectors. A particular focus is on the concepts of superposition and entanglement, as these are difficult-to-understand topics in quantum computing and quantum mechanics as a whole. To achieve this, a 1-qubit maximally entangled state is demonstrated with the Hadamard gate, as well as the 2-qubit maximally entangled state achieved from the Bell State circuit (Hadamard on the 1st qubit, followed by CNOT). Other topics that confused me personally are addressed (though I do hope others may find my explanation of these topics beneficial), such as the tensor product. Most of the visuals in this video are developed with the Manim library, a mathematical animation engine in Python. The probability distribution illustrated from a Bell State circuit was obtained using Qiskit, an open-source Python library developed by IBM that real quantum computer scientists use to simulate and run quantum circuits. This video is meant to provide a basic idea of the math behind quantum computing, particularly for interested beginners. I highly encourage further learning from Quantum Sense's series on quantum mechanics, for a continued math-focused series, or 3Blue1Brown's video on quantum computing, for more focus on how quantum computers can solve some problems faster than classical computers. Timestamps: 0:00 - Introduction 0:24 - Chapter 1: Qubits 1:30 - Chapter 2: Superposition 3:52 - Chapter 3: Quantum Gates 6:02 - Chapter 4: Entanglement 11:48 - Further resources