Quantum Information Science I, Part 1

• Models for classical computation
• History of quantum mechanics and quantum computation
• Computation must be robust against noise
• Physical and conceptual models of classical computation
• A brief introduction to computational complexity
• Universality of AND and NOT for boolean circuits
• Thermodynamics and computation - Maxwell's Daemon
• Szilard's engine and Landauer's exorcism of Maxwell's Daemon
• Reversible computation and the billiard ball model
• Reversible gates and circuits
• Mathematical pre-requisites for QM
• Mathematical representation of quantum states
• Physical examples of quantum states
• Global phases and quantum states
• The Bloch sphere representation of qubit states
• Rotating the Bloch sphere - Pauli matrices
• Common single qubit gates
• Unitary transformations - two definitions
• Unitary transformations - a third definition
• The Copenhagen interpretation of quantum mechanics
• Continuous rotations of the Bloch sphere
• Single-qubit rotation operators
• Composition of rotations and Bloch's theorem
• Towards multi-qubit states and gates
• Quantum states and the Bloch sphere - quick recap