Introduction to Quantum Computing

What is a qubit?

In this lesson, you will compare binary digits (bits) with quantum bits (qubits).

1. What are atoms made of?

An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element.

Bohr model of the atom (1913)	Helium atom, with nucleus and electron cloud distribution (1926 and current)
https://en.wikipedia.org/wiki/Atom#/media/File:Bohr_atom_animation_2.gif	By User: Yzmo - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=2246091

Atoms contain charged particles such as the positive nucleus in the centre, which is surrounded by electrons. These particles have other properties such as ‘spin’.

2. Representing a qubit on a Bloch sphere

When we work at the atomic or quantum scale, the properties of matter obey different laws. You will be aware of the ‘laws of physics’ regarding momentum and energy. Heavy trucks can cause more damage when they crash than bicycles. The more energy you put into a ball, the higher it will go when you throw it.

At the quantum scale, energy comes in ‘packets’ of a fixed size (which are called ‘quanta’). Electrons are somewhere near the nucleus of their atom, distributed in space according to a probability equation. Our common language of trucks and bicycles is replaced by new terms about chance and likelihood.

Therefore we need some new ways to think about atoms and quantum particles. One way to think about a quantum bit is to visualise a sphere with a dot on it.

As you begin to use a quantum computer, you can imagine working with a number of these spheres acting as your qubits. Your programming can cause the dot to move into different positions. To describe these positions, we need a frame of reference. This is given by the Bloch sphere picture:

Bloch sphere representation of a qubit

Using this picture of a qubit, the light blue dot can be located using the three angles (ϕ from the x-axis and θ from the z-axis, giving a qubit value of |ψ>. That’s right – qubit values are written in a funny way. You can see that if the little blue dot goes to the bottom of the sphere, the qubit value would be |1> (or just ONE if it were a binary digit). And if it went up to the top, the qubit value would be |0> (or zero if it were a binary digit). So you can see, a qubit can act like a binary digit, but there are lots of other values it can hold as well.

Exercise

This link provides a page of Bloch sphere qubits. Can you mark on each one where you think the blue dot should be to represent the given values?

If you are interested, qubit values are written using vector notation, so |0> = . This short form is called Dirac or ‘bra-ket’ notation. So you pronounce |0> as ‘ket 0’ and |1> as ‘ket 1’. We will use this notation to show qubit values to distinguish them from the values of a conventional binary digit.

3. Making a real qubit

Qubits can be made in several ways. IBM creates them from super-conducting junctions of Niobium, silicon and aluminium. The junctions have to be kept very cold. In fact, they are kept close to absolute zero, at a temperature of less than one degree Kelvin (-273° Celsius). Here is a diagram of such a qubit, and a video of how it was made.

Homework

Taking on board what you have learned about ‘ket’ notation, can you speculate how the state of a PAIR of qubits might be written? Try writing down some examples.

Credits

Billiard ball with dot: https://www.seyberts.com/pool-balls-single/aramith-blue-dot-cue-ball/

Bloch sphere representation of a qubit (from Smite-Meister CC BY-SA 3.0)