On Friday 30th September, I took part in Explorathon 2016 – a Europe-wide “extravaganza of discovery, debate and entertainment” to celebrate research being done in universities across Europe. As part of this, St Andrews hosted a jam-packed Explorathon night in the Byre, featuring museum torchlight tours, ukulele-based stand up comedy, solar cells made from raspberries and much more. Our research group presented “Quantum Digits and Dances”, an interactive show about quantum physics and our research. For those not able to make it to the show, here’s an outline of our show! Many thanks go to Jonathan Keeling, Brendon Lovett, Kyle Ballantine, Aidan Strathearn and Mhairi Steward for helping to make this happen.

*HC:*

Welcome to our show on quantum digits and dances! In the first half, I’m going to go all digital on you, explaining how quantum physics is paving the way to better computers. Then I’ll pass you across to Jonathan, who’s going to show you the moves to the quantum dances.

Before we explore quantum computers, let’s have a look at our normal, or classical computers. Classical computers, including PCs, iPhones and tablets are all made of many many tiny switches called bits. These bits can be 1 or 0 – like a switch which can be off or on. The more 1s and 0s we have in our computer, the bigger the problem it can solve.

We’re looking at an entirely different type of computer – a quantum computer. Unlike our classical computer, which is made up of 1s or 0s, quantum computers are made up of quantum bits, known as qubits.

Qubits have two special properties that make them different to ordinary bits, and the first one is known as superposition. Superposition means that our qubits can be 1 or 0, but they can also be part 1 and part 0 at the same time.

Let’s look at an experiment using light that demonstrates superposition. Like water, light is a wave that vibrates as it travels. Usually, light is unpolarised, which means that it vibrates in many different directions as it travels along. But if we pass our unpolarised light through a polarising filter, like this one here, then only the parts of light which vibrate in one plane are allowed through. The result is polarised light. Sunglasses contain polarising filters to reduce the amount of light reaching your eyes on sunny days.

Now, let’s see what happens when we have two polarisers. If our polarisers are lined up in the same direction, any light that gets through the first filter can also get through the second filter. But if we rotate one filter, then the light that gets through the first filter can’t pass through the second one, and the result is darkness, as we would expect.

The really interesting thing happens when we add a third filter at a diagonal to the first two. If we place the third filter on top of the first two, then no light is let through. But if the third filter goes in between the first two, then we get light!

Let’s unpack this. When the light goes through the first filter it is vertically polarised. Adding another filter at a diagonal on top changes the polarisation of the light – it is now diagonally polarised. We can think of diagonally polarised light as a superposition of horizontally polarised and vertically polarised light. When we add the third filter on top, the vertical part is filtered out, leaving just the horizontally polarised light to shine through. (Side note: this is explained in greater depth here)

This effect occurs because the light is in a superposition of states – part vertical, part horizontal. When we measured the state by placing the third filter on top, we destroyed the superposition. Superposition occurs in all sorts of quantum particles, not just light, and it’s one of the ingredients we need for our quantum computer.

The other special property we need to make our quantum computer work is called entanglement, and this can happen when we get two or more qubits together. To demonstrate this, I’m going to ask for two volunteers from the audience.

[Here I get two volunteers up on stage, and give each of them a packet. Inside each packet is a glove – one a left, the other a right. Both volunteers are asked not to look at their packets but to move to opposite sides of the stage, then one volunteer is asked to look in their packet and tell the audience which glove they have. Then the other volunteer is asked to say which glove they have, *without* looking in their packet.]

This glove demo is a bit like entanglement: in entanglement, we create a pair of entangled qubits and separate them, and as soon as the properties of one are measured, the other gains the corresponding properties. Unlike in our glove demo, the properties of the two entangled quantum particles aren’t set before the measurement is made. With the gloves, the left one was always the left one, we just didn’t know which it was until we looked in the packet.

Two entangled particles are both in two states at the same time – they’re both in superposition – but when we destroy that superposition in one particle by measuring it, the other particle also collapses into one state, even though we didn’t measure it.

This property of entanglement is something you can only find in the quantum world. But it has been measured – experimenters in the Netherlands succeeded in separating a pair of entangled particles by over a kilometre, then measuring the properties of one, instantly determining the properties of the other. (You can read more about it here, and the original paper is here.)

So far we’ve looked at two properties of the qubits – superposition and entanglement. Now let’s see how we can use those properties to build a more powerful computer.

Inside a quantum computer are many qubits, many quantum switches. Many of these qubits can all be entangled together, and this allows us to represent much more information in our quantum computer than we could in our classical computer. Each time we add a qubit to our quantum computer, we double the size of the problem it can handle.

To illustrate how powerful this is, let’s look at the parable of the rice on the chessboard. The parable goes that in ancient China, the inventor of the chessboard demanded payment from the Emperor. The inventor asked to be paid in rice: 1 grain of rice for the first square of the chessboard, 2 on the second, 4 on the third, and so on, doubling each time. Now this doesn’t seem too bad, but by square 18, we use up over 4kgs of rice. By square 36, the rice we would need would fill this auditorium. To fill the board, we would need

18,446,744,073,709,551,615 grains

– a heap of rice larger than Mount Everest.A quantum computer with just 64 qubits would be able to solve the same size of problem as a classical computer with over 18 quintillion bits! That’s what makes quantum computers so interesting, and gives them such great potential. And with that I’ll pass you across to Jonathan for some quantum dances.

*JK:*

We’ve seen the power that quantum computers may have, from the vast number of possible states they can have. This can be a problem when we try to understand the properties of materials made up of large numbers of particles – here we are talking not about 100s or 1000s or even 1000000s of systems, but 1 followed by 23 zeros. The numbers are huge; astronomical; in fact they’re bigger than astronomical. They’re even bigger than bankers’ bonuses!

This may seem hopeless, but actually there are ways we can understand quite a lot of materials, and over the past century, we’ve made enough progress to be able to predict reasonably well certain kinds of phases of matter. To begin to understand many of these things, it’s helpful to consider much simpler examples first. The really simple example that physicists spend a lot of time thinking about is the pendulum.

If we take two coupled pendulums, and set one moving, the motion seems at first to be complicated. What we can however do is try to find simple patterns of movement – for instance if we set them off moving together, they stay moving together and if we set them off in opposite directions, they stay like that.

We can say that moving one pendulum to set things off is like a combination of moving them both together and moving them in opposite directions. If we break down the initial movement into these parts, we find that we can understand the whole movement. This works for much bigger systems too!

So we can understand how many pendulums that are coupled to one another behave. What gets more tricky (and more interesting) is when we somehow feed energy into the system, and let it find its own state. Before considering lots of pendula, let’s first see what happens when we take one pendulum and feed energy in. There are various ways we could thing of doing this, but a particularly interesting case is when we shake the support up and down. This is known as Kapitza’s pendulum, after Pyotr Kapitza, a Russian physicist who thought about this concept. What we find is that at the right frequency, the state with the pendulum pointing down is unstable, and the state with it pointing up is stable.

The idea of the state pointing down being unstable is something you all know very well – it’s the idea behind a swing. When you swing your legs on a swing, what you are really doing is moving your centre of mass up and down, effectively making the pendulum (made out of you on the swing) longer or shorter. At the right frequency, it means that rather than just sitting at the bottom, you swing back and forward.

This idea – feeding energy into the system, and seeing what kind of motion results gets way more interesting when you have lots of coupled oscillators. We can’t easily build this with swings, but we can use a ready-made driven pendulum – a metronome. If we take many metronomes and put them on the table, then when we set them ticking then after a while, they’ll start to go out of sync because they’re not made perfectly. But if we put them all on a plank that’s allowed to move with the metronomes, then the metronomes come into sync, and stay in sync.

This sort of behaviour doesn’t just happen in physics labs – it happens in real life, too. On 1st January 2000, the Millennium Bridge in London opened. On its first day, thousands of people walked across it. And as they walked, they swayed back and forth – not because they were drunk, but because the bridge was coupling their motion, bringing them all into sync, just like the metronomes. In the case of the Millennium Bridge, the swaying was so severe that the bridge had to be closed so that engineers could make alterations that lessened the effect.

A similar effect can also exist in quantum systems, and here I have an example of this from the quantum world – a laser. In a laser, the idea is to have many atoms emit light all in sync. In fact the physics of the laser is very close to these examples. The light inside the laser is like the bridge, or the plank of wood. The atoms are like the metronomes, or the people on the bridge. By coupling them together with the light inside the laser, you make that atoms emit in a synchronised way. This self-reinforcing behaviour makes the light field stronger, until it has taken as much energy out of the atoms as it can.

One of the things we are looking at in our research is understanding other forms of this kind of lasing or locking behaviour, in cases where quantum physics is important, and trying to understand how quantum oscillators can be made to lock together.

*Featured image credit: Kenn Brown & Chris Wren / Mondolithic Studios*