What is superposition?
Before getting into qubits and operations, let's start with a simple example to understand how superposition works.
How can we describe superposition?
Imagine you have a cat and a box, and you want to describe the possible configurations of the cat and box system. For example, "the cat inside the box", "the cat next to the box", and so on.
Let's say that there are six possible configurations: "the cat on top of the box," "the cat inside the box," "the cat under the box,", "the cat next to the box," "the cat in front of the box," and "the cat behind the box." The configuration "the box inside the cat" isn't physically possible, so it's not in the list.
These six positions are the individual possible configurations of the system "cat and box." How could you describe the state of the cat and box system? You could sum up the individual positions, like this:
However, just the sum of the individual positions doesn't capture the full picture. You also need to consider the probability of finding the cat in each of the individual positions. For example, the cat is more likely to be next to the box than under it. So, you need to weight each individual position by its probability.
The state of the cat and box system is the sum of the six different positions of the cat respect of the box, weighted by the probability of finding the cat in that position:
The cat and the box are classical objects, so you can only observe them in one of the six possible configurations at a time. Cats and boxes live in the classical world, where objects can only be in one state at a time.
However, in the quantum world, things are different. A quantum cat and a quantum box could also be in all six states at the same time! This phenomenon is called superposition.
Quantum cats don't exist - as far as we know - but quantum particles do.
In the next unit, you'll explore superposition in quantum computing.