Quantum Systems from Group up

This talk reviews the modern formulation of the basic ideas of quantum mechanics. We start by explaining what quantum amplitudes are, how they lead to the idea of a quantum state and how these states evolve in time. We then discuss what happens when a measurement is made before describing correlated ('entangled') systems. Applying these ideas to two-state systems ('qubits') we point out that the complexity of computing the evolution of an N qubit system grows like exp(N)