What is superposition?

  • 3 minutes

Before we explore superposition in the context of qubits and quantum states, let's start with an example to help understand how superposition works.

In this unit, you learn how to describe the quantum state of a system that consists of a cat and a box.

How do you describe the quantum state of a system?

Imagine that 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
  • The cat behind the box

Other configurations, like the box inside the cat, aren't physically possible, so we don't consider those configurations.

These six configurations are the possible distinct states that we can find the cat-and-box system to be in. But because this is a quantum cat-and-box system, we can't accurately predict which of the six states that the system will be in when we take a look. How then do we describe the state of this system before we take a look at it?

Well, we describe the system as a superposition of all six possible states at the same time. In mathematical terms, the superposition state is a sum, or linear combination, of all six distinct states. It's a bit silly, but here's what a superposition of our cat-and-box system looks like:

Diagram of a cat and a box and the representation of six different positions of the cat with respect to the box.

But wait – there's more! Quantum states are probabilistic, so there's a certain probability that the cat-and-box system is found to be in each of the six possible states. And let's be honest, there's a greater probability that the cat is found to be inside the box than any of the other five states. Each state is weighted by its probability of occurring, so our superposition state looks like this:

Diagram of a superposition state of the system, which is the sum of the six different positions of the cat with respect to the box, weighted by the probability of finding the cat in each position.

Notice that the probabilities sum to 100% for all six states. This makes sense because we always find the system to be in one of the possible states when we observe the system. In real life, cats and boxes are classical objects, not quantum objects, so our example is a bit silly. But quantum objects, such as photons, electrons, atoms, and molecules, truly behave in this probabilistic manner in real life.

In the quantum world, we describe the state of a system as a combination of all the states that we can find the system to be in. This is the phenomenon called superposition.

In the next unit, you learn about superposition in the context of an actual quantum system, and the role that superposition plays in quantum computing.