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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.

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.