Basics of Quantum Computing 1

In this tutorial, I m leading you through the basic concepts of Quantum Computing. My goal is to smoothly introduce you to the concepts needed to understand Quantum Computing and walk you step-by-step through some examples. In later blog posts, I also walk you through some mathematical concepts but don’t worry this post is math-free.

My knowledge about the field of Quantum Computing does mostly come from the book “Quantum Computing verstehen” from Matthias Homeister. I also highly recommend this book for anyone who is interested in the field and able to read German. The material treated comes from the first chapter “Vom Bit zum Quantenregister”.

Alright, let’s get started and hopefully I manage to make you as excited about the field of Quantum Computing as I am.

Overview

• Introduction
• Bit vs QBit
• Generating the information wanted
• Good & bad properties
• Conclusion

Introduction

If you talk about Quantum Computing nowadays people often put you in the same category as following the flat earth society. In the category “weird”. In my opinion, the opposite will be the case at one point in time. Quantum Computing uses 2 of the most fundamental ideas of the 20th century, so why should combining these ideas be a bad decision?

• Quantum Mechanics
• Information Theory

These 2 key achievements lead to Quantum Technology and will shape the 21st century in some way. Given the fact that big companies like Google and IBM invest millions of Dollars in the development of Quantum hard- and software, my internal bayesian-brain tells me that now is a good time to start learning this topic. Also, the beauty of the idea of using the state of the smallest existing objects, to transfer information is limitless. It is per definition of the current state of our knowledge about physics not possible to get smaller.

Like anything in life, this is some kind of investment and only the future knows if studying this topic will pay back in some way to you.

Bit vs QBit

The “usual” laws of physics do not apply to objects as small as Quantum Particles. An important key takeaway is that these very small particles do have something called a spin which is either in one or in the other direction. A spin in one direction is called a positive spin while a spin in the other direction is called a negative spin. Do you see the equivalence to the usual Bit? A spin in one direction is encoded as a 1 whilst the spin in the other direction is encoded as 0. Yes it is simple as that!

Generating the information wanted

So how do we manipulate a Quantum-Bit to be either 1 or 0? Well, we just throw a bunch of photons (light waves) on it and it probably changes its state. What is important to know is that when throwing photons on our QBit we are never entirely sure that it changes its state to the state we want it to be. There is always some degree of probability involved. This is not necessarily bad since our stochastic world is full of randomness and especially for machine learning, data mining and statistics it is important to generate random numbers to model our random world. The random numbers generated by a Quantum Computer are often considered as “real” random numbers. This can be considered as the first advantage of Quantum Computers, since normal computers are not capable of generating “real” random numbers, only pseudo-random numbers. Pseudo-random means that these numbers are random to some degree but also not entirely since it is possible to calculate them beforehand which is somehow against the definition of randomness.

Good & bad properties

One of the most amazing properties of QBits is that we are in control of how probable the state is, in which we want the state to be. So, what do I mean with: “we are in control of how probable the state is, in which we want the state to be? Easy, if we only throw half of the photons on our quantum particle it does change its state to only 50%. If we throw 1/3 of our photons on our quantum particle? Exactly it does change to only 33%. Once we measure the state of our particle the probability collapses and we observe in which state the particle is.

Nice isn’t that amazing? Just take a bunch of particles, throw photons in its face and voila we have a quantum computer. Well, it is not that easy, we only talked about manipulating one single particle (1 Qbit). The problem is that these particles depend on each other and changing the state of one particle may or may not change the state of the particles next to it. So we need some degree of correction for these changes in the other particles and surprise, surprise this procedure is called a Quantum Computer’s Error Correction. Which is quite intense and will be the topic of a future blog post.

Conclusion

• Quantum Bits are quantum particles which have a spin in one or the other direction, this property is used as an analogy to the classical Binary Digit.
• To generate the information wanted, we throw a bunch of photons onto these quantum particles. The quantum particle’s spin is then changed to some probability.
• Unluckily it is not that easy since the spin-change of one particle changes the spin to some probability in another quantum particle.

I hope I could help you with my first blog post about quantum computing. In the case you find something odd, let me know and give me a comment.

Cheers, Alex