Quantum Mechanics Quick Reference

Quantum mechanics is a mathematical model of the physical world, which is built on a small number of postulates, each of which makes a particular claim on how the model reflects physical reality. All the rest of the theory can be derived from these postulates, but the postulates themselves cannot be proved in the mathematical sense. One has to make experiments and see whether the predictions of the theory are confirmed. To understand what the postulates say about computation, it is useful to think of how we describe classical computation. One way to do this is to say that a computer can be in one of a number of possible states, represented by all internal registers etc. We then do a number of operations, each of which takes the computer from one state to another, where the sequence of operations is determined by the input. And finally we get a result by observing which state we have arrived in. In this context, the postulates say that a classical computer is a special case of something more general, namely a quantum computer. More concretely they say how one describes the states a quantum computer can be in, which operations we can do, and finally how we can read out the result. In this respect, the claim of quantum mechanics is that this describes the most general form of computation that nature allows.