The eletromagnetic spectrum gives as a good foundation to start with simple and cheap quantum computing gates.
Lets start at the beginning. The radition of eletromagnetic waves
- Eletronic field “E” (not meant as energy)
- Magneic field “B”
are constructed by
- the wavelength ” λ” in m
- the frequency “f” in HZ (tells us how many waves are passing a point per second or in other words the inverse of time 1/s) as well as
- the kind emission. We focus on the visible light.
The wavelength λ is the product of frequency f and the speed of light c: λ = f · c. Let us assume that c is a constant (at least here on earth). If so the wavelength and frequency have a constant relationship.
- A high frequence shortens the wavelength
- A low frequence extends the wavelength
The visible light has a wave length of 380–800 nm. Compare Wikipedia here.
Overall the color depends on the wavelength which depends on the emited energy.
Now let us have a look on inference.
The hight of a wave is called the amplitude. It does not appear the the so far mentioned equations, because it describes the energy.
The transported photon energy “E” is the Planck constant “h” multiplied by the frequency “f”; E = f · h. This implies the frequency and the energy also has a constant relationship.
- A high frequence reduces the energy
- A low frequence increases the energy
Let us come back to inference. If at least two waves passing each other the amplitues get added. This inference is also called the superposition principle (also checkout the Bragg equitation).
Important: The direction of the wave need to be aligned and directed (aka polarisation)
A high amplitude is a higher amount of energy, with a lower frequency, resulting in a longer wavelength. This implies a higher amplitudes results in a longer wavelength as well as the color. The visible light has a wave length is between 380–800 nm, what gives as an encoding space of roughly 400 states per photon (light source).
But…
… we need a dimensional extension to make use of these states. 0 to 400 is one dimensional. Each additional dimensional at least halfs the states, because each of these states has to represent a combination of e.g., dimensions and their states. due to that bad…
This implies that we have to introduce multiple light source which interact with each other. We can come to a maximum entropy of 400^light sources – realistically 40^light sources. The light sources can be treated as dimensions. The quantum superposition on the unit circle can be aexpressed by the 400 / 40 wavelength (blue line).
