# 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 1-5 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

AND-gate
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

### 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

### 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

### 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 million-billion ($10^{17}$) 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 (if-then statements) on these quantum bits! • Connect quantum bits with a gates (if-then statements, e.g. AND, NAND, XOR, ...) • We invented a quantum computer! ### A sensibly sized simulation of nature • Entangled state of N-qubits 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 Quantum Computers

• Intel -- 49 qubits
• IBM -- 50 qubits
• Not quite enough... yet
• Superconducting states stable for around 100 micro-seconds
• Must stay very cold and isolated from environment
• Correcting errors requires additional qubits
• Need 100-500 for 50 atom simulation

### What about our hometown heros?!

D-Wave 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).