Recently a family friend asked if there were any applications to my research. To his disappointment, I answered “unless you’re a physicist at the Large Hadron Collider, no.”
But he pushed back “what about quantum computing?”
I do technically work in quantum field theory, and quantum is quantum, right? Well, not really. I calculate what happens when particles are accelerated to 99.999999% the speed of light and smashed together. As far as I know, this isn’t happening inside a quantum computer. So I felt pretty sheepish when, the following week, our group seminar happened to be on – you guessed it – quantum computing.
I had my vague ideas on what quantum computing was all about; by harnessing various quantum phenomena, we can make more powerful computers. A quantum state (a fancy way of talking about something small, like an electron) has some fairly strange properties. Superposition, for example, means that rather than having a very definite position, a quantum state has a probability distribution of where it might be. An electron isn’t simply in the middle of the room; it has a 50% chance of being somewhere in the middle, 40% chance of being somewhere in the corners and even a small chance of somehow being on the other side of the walls (please take this oversimplified example with a vat of salt). It’s easy to dismiss this as a consequence of us just not knowing enough about the electron; we might not know where it is, but the electron sure as hell knows where it is. But that isn’t what 100 years of theoretical and experimental results tell us. The electron really does live in many places at once. So, quantum computing must be using this property then. If the electron can be in many places at once, we must be able to do so many more calculations at one time! It’s true that this property helps differentiate quantum computing from classical computing, but this property alone doesn’t help much.
It must be entanglement then. You might have heard this called ‘spooky action at a distance’. The properties of one quantum particle can affect the properties of another, even if they are worlds apart. Let’s say we have two bags, each containing a red ball and a blue ball. We take those bags to completely different ends of the universe; they have no way of communicating with each other. I pull out a ball from bag one – it’s red. My alien counterpart pulls a ball from bag two – it’s blue. Nothing weird happening here. The alien had a 50% chance of getting either colour, right? So we repeat the experiment. This time I pull out a blue ball, the alien pulls out a red. Interesting – again we pulled out different colours, but it’s not too unlikely for this to happen twice in a row. So we repeat the experiment over and over again, thousands of times. Every time I pull out a red ball, the alien pulls out a blue one. Every time I pull out a blue, the alien pulls out a red. Did we actually only put one ball in each bag, and ensure we always had the opposite colour? No. We both had two balls. There should be no correlation between what I pull out and what the alien pulls out. But there is. This is entanglement.
Up until now, I was under the impression that this was the property that made quantum computing, well, quantum. The existence of entangled states allowed for computations that classical computers just cannot do. And that brings me back to the seminar, which claimed to be on the topic of magic. Yes, you heard me right. Magic. As is often the case with physics terminology, the word magic is maybe a little misleading. There’s nothing going on that is any more mystifying than superposition or entanglement. Magic is simply a way to quantify how difficult it is to simulate a quantum state on a classical computer. Why would there be any difficulty simulating a quantum state though?
If a deterministic classical computer wants to simulate our quantum bags each with a red and blue ball, it needs to hold four pieces of information: both balls being red, both blue, the first red and second blue, and vice versa. Meanwhile, a quantum computer can hold all of that information in a single state. For this reason, classical computers are unable to efficiently simulate a quantum state. Usually. There is a special type of quantum state called a stabiliser state, that is defined by being the exception to this rule. It is indeed a quantum state. It lives in the world of randomness and impossible corelations, yet it can be simulated by a classical computer just as efficiently as on a quantum one. This is the nightmare to the dream of quantum computing; why bother spending billions developing this new technology if we can simulate it on our desktop at home? We want a quantum computer that is able to do things a classical computer never will. In other words, we want a quantum computer that is free of stabiliser states. This lack of stabiliserness is called magic and it is essential to making quantum computers worth their while.
Quantising a lack of something else is not easy, and there are multiple proposed ways to measure magic, but what is clear is that magic is all around us. Recently, physicists measured magic in pairs of particles produced at the Large Hadron Collider.
So maybe my research won’t directly lead to the next groundbreaking invention. Maybe it won’t revolutionise the lives of my friends and family. But as it turns out, calculating probabilities for particle collisions might not be as distant from quantum computing as I’d previously thought.
Letters and Words 
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