At the microscopic level of atoms and electrons,
the world obeys the laws of quantum mechanics. One of the fundamental principles of quantum
mechanics is that it is possible to create super positions of different physical configurations. A simple example of this is a hydrogen molecule with only one electron. The electron could belong to the left proton or to the right proton. In fact, because it’s a quantum object,
it can belong to both. It’s in a quantum super position of being left and right. Now imagine I decided to encode binary information on the position of the electron. I call left 0, and right 1. This means that I can also create a quantum super position of 0 and 1. A quantum system that has two basic states is called a quantum bit or qubit. To define the value of a qubit, I need to specify what quantum super position it’s in. In general, the qubit can be in A0 plus B1. This becomes very interesting when one considers more than one qubit. For example, with two qubits, the basic states are 0-0, 0-1, 1-0 and 1-1, but in fact I am allowed to make any super position of these four states. So in general, I must write A0-0 plus B0-1, plus C1-0 plus D1-1. Now you see that to specify the state of two qubits, I need to give four numbers, A, B, C and D. If I had three qubits, I would need
eight numbers and so on. Every time I add a qubit, I need twice as many numbers to describe the collective state of these qubits. Notice the difference with the case of classical bits. There, each state is completely specified given the value of each bit. In the quantum case, I need to specify which super position of the two to the power N possible states
I have created. If I have three hundred qubits, I would need 2 to the power of 300 numbers. There’s not even enough particles in the universe to record so many numbers. This gives you a sense of the enormous complexity one can find in the quantum realm and the aim of quantum computing is to harness this complexity to perform certain calculations much faster than any standard computer ever could.