An introduction to quantum computing

This post gives a beginner their first look into quantum computing. It covers all the basics required to understand how quantum teleportation works. For the teleportation algorithm itself see the second part of this series here, and for how it is implemented using Qiskit on a real quantum computer, see the third part here. For this tutorial I will assume a basic understanding of linear algebra and braket notation. Although I will use braket notation throughout, all of this could also be though of in terms of normal matrix notation too.

Qubit states

As I am sure you are all familiar with, bits on a classical computer can be stores as either a 0 or a 1. What makes quantum computing different is that we can also have a bit that is in a superposition of 0 and 1.

We will define the two possible measurements as the kets |0> and |1>. The |0> state is the state in which we have 100% probability of measuring 0, and the |1> state is the state where we have 100% probability of measuring 1. All other states can then be represented as a linear combination of these.

The coefficients a and b represent the probability amplitudes of measuring each state. So, if we have this state we would have a probability equal to a² of measuring 0 and b² of measuring 1.