What in the world is topological quantum matter? – Fan Zhang

What in the world is topological quantum matter? – Fan Zhang


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.

100 thoughts to “What in the world is topological quantum matter? – Fan Zhang”

  1. i always wish these vids would go more in depth. You've introduced topology, great, but didn't really explain how it can apply to physics.

  2. Hey "Tell Me This," I may be type #873a: One who understands the present spectrum of Quantum Physics on an academic level, feeds three cats who never wander near boxes, remains apolitical, served in the military, but doesn't own a handgun, shops at thrift-stores, drinks well-water (can't fluoridate me haha), and finds it humorous, albeit pitiful that modern man has become so impressed with himself.
    I have been using topological ointments for years. LOL

  3. You can also use topology to explain the brain's connections:
    https://www.newscientist.com/article/mg23531450-200-the-brains-7d-sandcastles-could-be-the-key-to-consciousness/

  4. The vid is GRT..but the example which u gave of the mug nd the donut is wrong as the mug has two holes not one..

  5. Waiting for a video for quantum computers, introduction and its implication in the world of computing (both negative and positive implications.)

  6. Topological field theory has a hidden danger. Reductionism has never worked for theoretical physics. This is why the LHC's validation of the Standard Model's predictions didn't lead to deeper theoretical devices. Topology gives enormous freedom to define infinitely many independent variables and to constrain the degrees of freedom an arbitrary mathematical object's motion may take. There is a real risk that this model will generate confirmation bias when all attempts at a reductionist interpretation appear to work. Anomalies would be difficult to detect, much less to discard.

  7. The example confused me a little bit… You have the doughnut, the coffee mug, and the pretzel. You said that you'd have to cut holes into the doughnut to make it a pretzel but that's not true. You can stretch and fold the doughnut into a pretzel shape. The main take away of that example was that the objects will conduct the same as long as you don't break the object or do anything to break the object's exterior circuit correct? I'm just confusing myself on the example and folding doesn't change the shape…. I actually just answered my own question…. Alright

  8. This was probably one of the best/most manage explanations I've heard about on this topic. Thank you for sharing!

  9. Hi, pls be patient with me, for i know nothing about quantum physics… but after watching, i have a question:
    Why do the orbits in the outer layer become open / connected? don't these electrons revolve around a single atom, as the ones in the middle? how do you split an atom and maintain half of it's orbitals? thx 🙂

  10. Ya.. this video doesn't say that elections move super slowly when travelling over distances. I believe electrons can be out walked an a typical DC current. not sure tho.. However, Obviously in our new tiny devices,, distance isn't an issue as it was just 20+ years ago. Thanks for reading.. like and subscribe.

  11. Topo-logical comes from Τοπος and λογος, which is Ancient Greek.

    Τοπος means either

    1. Place/Space

    or

    2. An summary of points in flat level or space with a common property/characteristic

  12. So 100% efficiency is possible? The theory is brilliant but we can only believe it practically proved. How can you make the atoms move in a enclosed structure like that?! I wanna know!!!!

  13. Check out 03:56; the answer to life, the universe and everything!
    Douglas Adams' Deep Thought is a quantum computer.

  14. How come a cup of coffee has the same holes with donut when the cup of coffee has two holes? (If you look from the top)

  15. Create more cartoons about physics, neuroscience, astrophysics and artificial neural networks. Please TED-Ed.

  16. To a topologist, the letter T is like helicopter blades, a fidget spinner, and if you think hard enough, a person.

  17. Think of it this way. It can allow for stronger processing in computers because in topology, no matter how much you change the shape of the electrical waves around it, it stays working. Topology focuses less on holes than the gaps around a place. If there were gaps in the ground at a race, of course it’d be harder to end up at the finish line than if everything in the race is smooth. Hence greater efficiency.

  18. Idk why but this reminds me of Draco Dormiens Nunquam Titilandus which is Latin and the Hogwarts motto which is Never Tickle A Sleeping Dragon Im pretty sure I know a few words in Latin but its all thanks to google translate

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