"Thinking Quantum": Lectures on Quantum Theory

Abstract: We present a conceptually clear introduction to quantum theory, deriving the theory from scratch from the point of view of quantum information. Different subsets of these lectures were taught to a wide variety of audiences, including exceptional high-school students in the International Summer School for Young Physicists (ISSYP) at Perimeter Institute, 2nd-year physics undergraduates at the University of Toronto, and 4th-year physics and math undergraduate and graduate students at Brock University. The lectures are completely self-contained, including all the necessary mathematical background: complex numbers, linear algebra, and probability theory. They cover topics such as the axioms of quantum theory, qubits, superposition, entanglement, the uncertainty principle, quantum gates, unitary transformations and evolution, interpretations of quantum mechanics, the no-cloning theorem, quantum teleportation, quantum algorithms, Hamiltonians, the Schrodinger equation, canonical and path integral quantization, quantum harmonic oscillators, wavefunctions, and much more. The lectures also contain 163 computational exercises and proof-based problems.