Quantum theory has been puzzling physicists and philosophers since its birth in the early 20th century. However, starting in the 1980s, rather than asking why quantum theory is so weird, many people started to ask the question:

What can we do with quantum weirdness?

In this book we not only embrace this perspective shift, but challenge the quantum icons even more. We contend that one should not only change the kinds of questions we ask about quantum theory, but also:

change the very language we use to discuss it!

Before meeting this challenge head-on, we will tell a short tale to demonstrate how the quantum world defies conventional intuitions …

The Penguins and the Polar Bear

Quantum theory is about very special kinds of physical systems – often very small systems – and the ways in which their behaviour differs from what we observe in everyday life. Typical examples of physical systems obeying quantum theory are microscopic particles such as photons and electrons. We will ignore these for the moment, and begin by considering a more ‘feathered’ quantum system. This is Dave:

He's a dodo. Not your typical run-of-the-mill dodo, but a quantum dodo.We will assume that Dave behaves in the same manner as the smallest non-trivial quantum system, a two-level system, which these days gets referred to as a quantum bit, or qubit. Let's compare Dave's state to the state of his classical counterpart, the bit. Bits form the building blocks of classical computers, whereas (we will see that) qubits form the building blocks of quantum computers. A bit:

1. 1. admits two states, which we tend to label 0 and 1,

2. 2. can be subjected to any function, and

3. 3. can be freely read.

Here, ‘can be subjected to any function’ means that we can apply any function on a bit to change its state. For example, we can apply the ‘NOT’ function to a bit, which interchanges the states 0 and 1, or the ‘constant 0’ function which sends any state to 0.