Why quantum computing?

Random bits and qubits

Multiple qubits

The no-cloning theorem

Superdense coding and teleportation

Quantum gates and circuits

Deutsch's algorithm and the Deutsch-Jozsa algorithm

Simon's algorithm

The quantum Fourier transform and its inverse

Phase estimation

Computational number theory

Shor's algorithm for order finding and factoring

A simple searching algorithm

Grover's search algorithm

Quantum computational complexity theory

Density operators

General measurements

Distance and similarity measures

Quantum channels

Impossibility of quantum bit commitment

Quantum key distribution

Possibility of quantum money

Nonlocal games

My favourite nonlocal games