Table of Contents

• 1: Historical context: Blackbody radiation, photoelectric effect, limitations of classical physics.
• 2: Basic concepts: wave-particle duality, quantization.
• 3: Wavefunctions and probability amplitudes
• 4: Hilbert spaces and linear operators
• 5: Schrödinger's equation (time-independent and time-dependent)
• 6: Observables, expectation values, and the measurement postulate
• 7: Uncertainty principle
• 8: Free particles and wave packets
• 9: Particle in a box (1D, 3D)
• 10: Harmonic oscillator
• 11: Hydrogen atom
• 12: Entanglement
• 13: Bell states and non-locality
• 14: Tensor products
• 15: Definition, superposition, Bloch sphere representation
• 16: Single qubit gates (Pauli operators, Hadamard, etc.)
• 17: Quantum vs. classical bits
• 18: No-cloning theorem
• 19: Building quantum gates from universal sets of gates
• 20: Multiple qubit gates (CNOT, SWAP, etc.)
• 21: Circuit diagrams
• 22: Deutsch-Jozsa algorithm (simple example of quantum advantage)
• 23: Grover's search algorithm
• 24: Shor's factoring algorithm (overview and implications)
• 25: Types of errors in quantum systems
• 26: Basic error correction codes (repetition codes, stabilizer codes)
• 27: Threshold theorem
• 28: Superconducting circuits
• 29: Trapped ions
• 30: Photonic systems
• 31: Topological qubits (brief overview)
• 32: Noisy Intermediate-Scale Quantum (NISQ) era
• 33: Variational Quantum Algorithms (e.g., VQE for chemistry simulations)
• 34: Challenges of noise and decoherence
• 35: Quantum simulation (materials, chemistry)
• 36: Quantum cryptography and communication
• 37: Quantum machine learning