Quantum computing: a nerdy introduction
If you are like me, you would like to understand quantum computing a bit better, but instantly get bogged down in the notation and the seemingly conflicting descriptions of how quantum computer work. I’m not a physicist, but I’m also not afraid of a little maths and I hope you are not either. So in this series of blog posts I will be going through some key concepts of quantum computers, starting with some basics and building from there to an understanding of how we may use quantum computers to change the world and when that might be. When I first studied quantum computing at university I didn’t pay very much attention. The idea seemed so ludicrous that it didn’t seem likely to be of any relevance within my lifetime, if ever.
So what changed?
Well those familiar with semiconductors will know all about Moore’s law that stated that the price of a transistor will halve every 18 months. This rule has held true for most of my parents’ lifetime and has taken the transistor from something that existed in a lab, to the billions contained in our mobile phones. Transistors have got exponentially cheaper and they have also got smaller, with modern technologies having just a few nanometres across the gap that makes or breaks the transistor and switches it from 1 to 0. With transistors that small, there are only a few hundred atoms across that gap.
The progress in transistor technology didn’t happen automatically, but Moore’s law has driven investment in research and innovation to deliver improvements in that technology on that schedule. It turns out that quantum computers have a Moore’s law of their own. We have seen continuous improvements in the number and quality of qubits over the last few decades since I graduated from university, and the investment is heating up. We are now in an arms race between the US and China with Europe tagging along. The global power that first cracks quantum computing will define the geopolitical shape of the world to come.
We need to start caring about quantum computers. They will change everything from the way we store intellectual property to the way we move money. They will change the way we design new products such as cars and mobile phones by enabling leaps in battery and surface technology and clean energy. That will come soon, but it can’t come fast enough. I write this as storm Darragh batters the UK and part of my roof has blown off for the third time. We need to change everything about the way we live if there is a future for our grandchildren.
A quantum overview
So let’s get started with a bit about quantum mechanics. The following blog takes us from our understanding of waves to an understanding of quantum superposition and entanglement. We also look at the notation used in quantum computing to get us familiar with the way physicists describe their systems.
→ Concepts of quantum computing
Building upon that, the double slit experiment is a great way of understanding the trickier aspects of wave-particle duality. It helps us to understand that the qubit is not simply in two states at once, but it is in a superposition of two states.
→ Quantum mechanics: The double slit experiment
Quantum uncertainty is one of the trickier concepts of quantum computing. We don’t know what the answer is going to be, but doesn’t that mean there is something about the universe that we haven’t understood yet? Well no, that is called the hidden variable theorem, which I discuss here.
→ Hidden variable theorem and quantum uncertainty
Now that we understand a bit about quantum mechanics and how we express state in a quantum computer, we can start to think about what a quantum algorithm looks like.
One key algorithm is Shor’s Algorithm. Peter Shor showed that with a sufficiently large quantum computer you can quickly and easily factorise any large number N. This is very hard with a classical computer, but can be done in theory with a quantum computer quickly
