Software but Quantum - Part 2

Well hello there.

We'll be picking up on the first part of this series, and get into the fundamental idea of superposition, which is super important to learn when it comes to Quantum Computers solving real-life problems.

Recall in the last post, we talked about Wave-Particle Duality (WPD) and Wavefunctions. These two are different things. The Wave that light behaves as is real, but the Wavefunction is a mathematical idea that we use to determine where the electron might be in an atom.

Now, a question you might have is why we can't just say where the electron will be. Why are we using a Wavefunction to tell us where it probably will be?

This comes down to something called the Heisenberg Uncertainty Principle (HUP). The HUP tells us that it's impossible to accurately know the position and speed of a particle at the same time.

For example, we know that an electron behaves as a wave, because of the Double-Slit Experiment (read the last post if you don't know what this is). If the electron behaves as a wave (the real kind), the probability that we'll find the electron is highest where the wave has peaks.

This might seem kind of arbitrary but it makes sense if you think about it. A wave represents energy travelling through space. The peaks represent where the highest amount of energy will occur. We know an electron or photon or any particle for that matter has energy. So that's were we'll probably find the particle.

So the HUP tells us that if we look at a wave, we'd know the speed of the particle

Let v be the velocity
Let λ be the wavelength
Let p be the momentum of the particle
Let h be Planck's constant

p = h / λ

p = mv

v = p / m

v = h / λm

So, we don't know where the particle is (due to the multiple peaks) but we do know the speed of the particle.

Alright, let's say we do look at the wave and try to figure out where the particle is. This is where things start to get weird. The wavefunction collapses entirely, leaving us with a single position of a particle.

For example in the below picture, you know where the rollercoaster is but not how fast it's going.

This is called Superposition and Wavefunction Collapse (WFC). Nobody really knows how WFC works, or how the Wave knows where to put a particle when someone looks at it. This is also the idea behind Erwin Schrodinger's thought experiment involving a cat.

The next part of this series will talk about how superposition let's us do math beyond the regular bits of 1 and 0 that we use in classical computers.

Cheers