##### Basic Science

# What in the world is topological quantum matter?

What if electricity could travel forever without being diminished? What if a computer could run exponentially faster with perfect accuracy? What technology could those abilities build? We may be able to find out thanks to the work of the three scientists who won the Nobel Prize in Physics in 2016. David Thouless, Duncan Haldane, and Michael Kosterlitz won the award for discovering that even microscopic matter at the smallest scale can exhibit macroscopic properties and phases that are topological. But what does that mean?

First of all, topology is a branch of mathematics that focuses on fundamental properties of objects. Topological properties don’t change when an object is gradually stretched or bent. The object has to be torn or attached in new places. A donut and a coffee cup look the same to a topologist because they both have one hole. You could reshape a donut into a coffee cup and it would still have just one.

That topological property is stable. On the other hand, a pretzel has three holes. There are no smooth incremental changes that will turn a donut into a pretzel. You’d have to tear two new holes. For a long time, it wasn’t clear whether topology was useful for describing the behaviors of subatomic particles. That’s because particles, like electrons and photons, are subject to the strange laws of quantum physics, which involve a great deal of uncertainty that we don’t see at the scale of coffee cups.

But the Nobel Laureates discovered that topological properties do exist at the quantum level. And that discovery may revolutionize materials science, electronic engineering, and computer science. That’s because these properties lend surprising stability and remarkable characteristics to some exotic phases of matter in the delicate quantum world. One example is called a topological insulator. Imagine a film of electrons.

If a strong enough magnetic field passes through them, each electron will start traveling in a circle, which is called a closed orbit. Because the electrons are stuck in these loops, they’re not conducting electricity. But at the edge of the material, the orbits become open, connected, and they all point in the same direction. So electrons can jump from one orbit to the next and travel all the way around the edge.

This means that the material conducts electricity around the edge but not in the middle. Here’s where topology comes in. This conductivity isn’t affected by small changes in the material, like impurities or imperfections. That’s just like how the hole in the coffee cup isn’t changed by stretching it out.

The edge of such a topological insulator has perfect electron transport: no electrons travel backward, no energy is lost as heat, and the number of conducting pathways can even be controlled. The electronics of the future could be built to use this perfectly efficient electron highway. The topological properties of subatomic particles could also transform quantum computing.

Quantum computers take advantage of the fact that subatomic particles can be in different states at the same time to store information in something called qubits. These qubits can solve problems exponentially faster than classical digital computers. The problem is that this data is so delicate that interaction with the environment can destroy it. But in some exotic topological phases, the subatomic particles can become protected. In other words, the qubits formed by them can’t be changed by small or local disturbances.

These topological qubits would be more stable, leading to more accurate computation and a better quantum computer. Topology was originally studied as a branch of purely abstract mathematics. Thanks to the pioneering work of Thouless, Haldane, and Kosterlitz, we now know it can be used to understand the riddles of nature and to revolutionize the future of technologies.