Quantum Computing For The Curious

Think of all the small around you. I’m not talking about your phone, your little notebook, or your drawer. Think so small that you can’t see it. Atoms, molecules, subatomic particles. What if I told all of the smallest things to rely on one set of laws that govern all of its actions. This is quantum physics, which is how our universe operates.

In quantum physics, electrons are usually regarded as a wave function. This wave is not a real physical thing, like water or soundwave. The wave function is an abstract mathematical wave.

This wave-function can predict what subatomic particles do well. For us to understand it and have real-world properties we need to turn it into a probability distribution. You can achieve this by squaring the amplitude (height) of the wave.

The probability distribution shows you where the electron is most likely to be, the higher the amplitude (height) of the wave the higher chance the electron will appear there.

You might be asking yourself what is the point of the wave function? Are we not looking at electrons?
When most of us hear electrons we think of a negatively charged atom. In quantum physics, electrons are initially viewed as waves. The Double Slit experiment presents this idea well.

Double Slit experiment:

Physicists used this experiment to show how a particle is a wave. Even though we can’t see the wave, this experiment results in the properties of waves.

In this experiment, you have 3 blocks with 2 slits (narrow holes) in between and along the back wall.

Imagine you are spraying a paintball gun, and you are trying to get it through the slit. With some questionable aim on your part, you hit the front 3 boards a couple of times, but you did manage to get some through the slit. Below are your results.

Double Slit Experiment W/Paintball Gun

From your center position, there are two possible areas where you can land the paint on the back wall due to how narrow the slit is.

Unlike the paintballs, the electrons will not behave in the same way. When the electrons fire, they behave differently. They create multiple patterns on the back wall, not just the 2 you saw from the paintball version.

Looking at the example below, it does not make sense how all these patterns emerge when you fire in a straight line, from a central position, through 2 narrow holes.

Double Slit Experiment W/Electron

In reality, when an electron fires, it is completely different than our paintball gun; it fires in waves.

When the waves spread, they do not create a linear pattern. They create something called interference pattern (more than 2 patterns), which is something that can only be found in waves.

Electron Wave Representation

When the waves reach the slits, it creates two other waves that go on to overlap one another, creating a property distribution, which if you recall is where the electrons are most likely to be.

Electron Wave Overlap

As confusing as this image might be, all you need to understand is that the overlap of the waves above creates more than just 2 patterns on the back wall.

At the points where the waves overlap, it is where the electron is most likely to be. At points where the waves do not overlap on the backboard, it where you are least likely to have your electrons.

The image above shows you all the points of overlapping. If you look closely the points on the wave that had the most overlap building up to the backboard are the ones with the highest probability.

Understanding this wave is a good representation of how quantum computers work.

What are bits ?

Bits are the most basic form of information and it can only be in one state at a time. It is like a light switch, it is either on or off.

This is also where the terms spin up and spin down come from. This refers to energy within an electron. With spin-up you have more energy making it associated with light and spin-down has less energy making it associated with darkness.

What are Qubits?

Qubits, on the other hand, can be in both states at once. This is called superposition.

Superposition allows for the qubit to run more possibilities as it has exponential more possibilities.

All possibilities of 4 qubits

You can think of it like it as spinning a coin. During the spinning, you do not know whether it is heads or tails as it can be both.

Going back to the waves, you think of it as 2 waves adding together. If you look to the left of the equal sign, you find that that the 2 high points on the waves are the ones that are in current superposition.

How are Qubits Connected?

Think of your friend giving you a call, regardless of the distance you receive it as both are connected to cell towers. When your friend calls your number, you get a receiving call screen, which looks kind of looks like this ⬇️.

In quantum computing, qubits are all interconnected. This connection is called entanglement. This connection between the two-electron waves makes it so when you measure one, you know instantly know the value of the other. Same with how you received a pop-up screen from your friend’s call.

The electrode — which is like you the cell towers that connect your phones — is what controls the connection of two qubits.

In the example above, there is a wave function that tells you everything about two particular electrons. Even if these two waves away from each other, they are still linked, similar to your connection with a friend in another country.

Once these waves are linked, they can be billions of miles away and still process information, this is called non-locality. Unfortunately, this can not be used for communication as its measurement will give you random results.

How Is Information Processed In Quantum Computers?

In quantum computers, there is a thing called transistors, which control the flow of electrons.

Sometimes the transistor has a barrier that blocks off information from going through. This barrier is similar to your mom letting you have too many cookies.

In quantum physics, the electron wave can pass through the barrier. When the electron wave meets the barrier it slowly decays the wave exponentially, making it more likely for the said wave to have an electron on the other side.

This is kind of like how you would sneak out of bed at night to get one last cookie. This process is called quantum tunneling.

Why is it so fast?

There is a process called superconducting because of the very low temperature (-273 degrees Celcius) it creates a system where the electric charges can pass through very easily. In essence, it is like removing traffic from a highway.

Heisenberg Uncertainty Principle:

The uncertainty principle says that we cannot measure the position and the momentum of a particle with absolute precision.

Momentum: measured by the amplitude or height of the wave

Position: measured by the wavelength of the wave

Where does the Uncertainty Come From?

The uncertainty comes from only knowing the position, momentum, or not knowing any at all.

In the example above, this is a sine wave where you only know the momentum. You know you wavelength because it is a single value, but your position has an equal chance of being anywhere on that wave.

With this example, you only know the position or the height of the wave. The problem here is you can not know the momentum, unless it is a perfect sine wave.

This picture above shows what we know and what we don’t know when from looking at a wave. These are not a limit of our measuring apparatus, this is a fundamental property of the universe. If you recall, our world is made of matter, which is made of atoms, which are made of sub-atomic atoms. These subatomic atoms are made of waves until they are measured.

Applications:

With quantum computing the possibilities are endless. From more accurate whether predictions to accelerating drug discovery, to financial markets. Its ability to simulate quantum mechanics and run through so many different possibilities at once can helps optimize and improve everyone life globally.

Key Takeaways:

1. The world is based on quantum mechanics

2. Objects are described with wave functions

3. Particle wave duality is about how a wave collapses and turns into a

4. A bit is an information that is processed as a 0 or 1

5. A qubit can be in both states of 1 and 0

6. Once connected qubits instantly react to one another

7. Measurement of both position and the momentum of a particle with absolute precision is not possible.