Quantum Computing
... from transistors to quantum supremacy
Slides by Nik Hartman. Originally for Nerd Nite YVR #37.
Quantum supremacy

When a quantum computer can accomplish something a classical computer cannot.

Likely to show up in your newsfeed in the next 15 years.
First  Let's talk classical computers
All the computer hardware we know and love today is based on the semiconductor transistor .
Transistors = Semiconductor Junctions
Now we can do calculations with binary numbers!
Before we do calculations... let's learn to count
$2^2=4$ 
$2^1=2$ 
$2^0=1$ 
SUM 
0 
0 
0 
0 
0 
0 
1 
1 
0 
1 
0 
2 
0 
1 
1 
3 
1 
0 
0 
4 
1 
0 
1 
5 
1 
1 
0 
6 
1 
1 
1 
7 
Transistors to logic gates (ifthen statements)
ANDgate 

A 
B 
OUTPUT 
0 
0 
0 
1 
0 
0 
0 
1 
0 
1 
1 
1 
many possible logic gates can be created
EXAMPLE: 2 + 3 = ??? (or 010 + 011 = ???)
2 + 3 = 5
but computers do more than add numbers...

Many of the hardest computational problems are simulations of nature.

Often we can be simplify and accept approximate results

What about exact simulations of nature?

To describe nature exactly we need quantum mechanics.
example: interesting (but difficult) simulation

Simulating molecules for better/safer drugs

Quanum mechanics determines molecule shape, interactions, and efficacy
Why is simulating quantum mechanics difficult?
Superposition
A fundamental property of the very small world.

The only results we can measure are $\uparrow$ or $\downarrow$

Before measurement it can exist in a combination (superposition) of both states.
superposition = $a \cdot \downarrow + b \cdot \uparrow $

$a$ and $b$ are the probabilities of measuring the atom pointing down or up
Superposition  An Analogy*
superposition = $\frac{1}{2} \cdot LAMB + \frac{1}{2} \cdot LOBSTER $

What happens when the waiter asks (measures) what you would like?

Your uncertain order (superposition) collapses into a single decision.

If this scenario could be recreated over and over  50% of the time you choose lamb, 50% lobster
* without any dead cats
more is different  and may be impossible

A system of N atoms has $2^N$ possible configurations

$ 2 \cdot 2 \cdot 2 \ldots 2 \cdot 2 \cdot 2 = 2^N $

Any simulation must keep track of all of these configurations to determine most probable measurement result

Adding another atom doubles the processing power needed
ok.. let's double the processing power!
One limit on this plan

1 billion operations per second => smartphone

Uses about as much power as an LED light bulb

Today's supercomputers: 100 millionbillion ($10^{17}$) operations per second

About as much power as New York City

$2.5 million CAD in electricity per year

That is roughly 1 million billion ($10^{15}$) Joules per year

World produces about 100 billion billion ($10^{21}$) Joules per year
transistor size limits

Modern CPU has 10 billion ($10^{10}$) transistors.

Supercomputers use 100,000 processors in parallel.

About $10^{15}$ transistors in total.

Number of cells in 10 people.

Probability of electron(s) spontaneously hopping across $\sim e^{kL}$

L = channel length

k = electron energy
What do we get for all that power?
Simulate interactions between 45 atoms
Using current technology and all of the world's electricity, we can get to about 70 atoms.
Richard Feynman suggests a way out
If simulating quantum mechanics on a classical computer is too costly, build a quantum computer.
Transistors + Quantum Mechanics = quantum bits

Always 0 or 1

Channel open or closed

Any superposition of 0 and 1

Atom up or down
A quantum processor needs more than one qubit

Qubits can be combine to make more complicated superpositions

Single atom superposition:
$$superposition = a_0 \cdot \downarrow + a_1 \cdot \uparrow$$

Many atoms forming a single superposition are entangled.

Multiple (3) atom entangled superposition:
$$superposition = a_0 \cdot \downarrow\downarrow\downarrow + a_1 \cdot \downarrow\downarrow\uparrow + a_2 \cdot \downarrow\uparrow\downarrow + a_3 \cdot \uparrow\downarrow\downarrow + \\
a_4 \cdot \downarrow\uparrow\uparrow + a_5 \cdot \uparrow\downarrow\uparrow + a_6 \cdot \uparrow\uparrow\downarrow + a_7 \cdot \uparrow\uparrow\uparrow$$

We can perform logical gates (ifthen statements) on these quantum bits!

Connect quantum bits with a gates (ifthen statements, e.g. AND, NAND, XOR, ...)

We invented a quantum computer!
A sensibly sized simulation of nature

Entangled state of Nqubits is a superposition of all $2^N$ configurations.

$$superposition = a_0 \cdot \downarrow\downarrow\downarrow + a_1 \cdot \downarrow\downarrow\uparrow + a_2 \cdot \downarrow\uparrow\downarrow + a_3 \cdot \uparrow\downarrow\downarrow + \\
a_4 \cdot \downarrow\uparrow\uparrow + a_5 \cdot \uparrow\downarrow\uparrow + a_6 \cdot \uparrow\uparrow\downarrow + a_7 \cdot \uparrow\uparrow\uparrow$$

Quantum computer needs only N qubits to simulate N quantum mechanical objects.

About 50 qubits can do something impossible for a classical computer!
Real Qubit

Superconducting Ring

CW current = 0

CCW current = 1

Built on pieces of semiconductor

Easy to connect many qubits

Just like connecting many transistors in our classical computer
Real Qubits
Real Quantum Computers

Intel  49 qubits

IBM  50 qubits

Google  72 qubits

Not quite enough... yet

Superconducting states stable for around 100 microseconds

Must stay very cold and isolated from environment

Correcting errors requires additional qubits

Need 100500 for 50 atom simulation
What about our hometown heros?!
DWave makes quantum annealing processors. Not universal quantum comptuers.

Define interactions between qubits.

Example: spins have lower energy when pointed in the same direction as neighbor(s).

Start with high energy state.

System evolves to lowest energy state over time.
stay tuned for quantum supremacy!