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Quantum MechanicsandQuantum Computation

- Sarah Brandsen

- If quantum mechanics hasnt profoundly shocked

you, you havent understood it yet. - -Niels Bohr

Outline

- What is Quantum Mechanics?
- Phenomena
- Quantization
- Wavefunctions and Schrodingers Cat
- Quantum Computing
- What is Computing?
- Why might Quantum Computers be useful?
- National Security and Quantum Computers
- Quantum Key Distribution (QKD)
- Polarized Photons, Heisenberg Uncertainty,

No-Cloning Theorem - Is QKD a perfect form of encryption?
- When will we have quantum computers?

What is Quantum Mechanics, really?

- Our attempt to understand the universe on

extremely small (nanoscopic) scales - This leads to strange and unintuitive results-
- Momentum and energy can be quantized
- Light and matter can both exhibit wave and

particle behaviour

Most Famous Observation in Physics- Schrodingers

Cat

- In fact, the mere act of opening the box will

determine the state of the cat, although in this

case there were three determinate states the cat

could be in these being Alive, Dead, and Bloody

Furious. - - Terry Pratchett

Set-up for Schrodingers Cat

- Place cat in box with a purely random radioactive

source that has 50 of going off (killing the

cat) within an hour - At the end of the hour, right before you open the

box, the cats state is completely unknown - Therefore, the cat is considered to be both alive

and dead at the same time until it is observed.

Wavefunction

- The wavefunction represents all possible outcomes

and their probabilities

Square this to find probability of cat being

alive 50

State of cat being alive

Measurement and Zombie Cats

- If cats can be in superpositions of dead and

alive, why dont we see zombie cats? - According to a standard interpretation,

measurement collapses the wavefunction into a

single state!

Quantum Computing- Active Research based on

Quantum Mechanics

What is computing?

- Goal-oriented activity
- Store information in bits (0 or 1) and processes

the information similarly to computation by hand - Very effective for many tasks, but has time

limitations for other tasks

Example- Computer Chess Game

- Input- Your move of the chess piece
- Process- Based on your move, the computer

calculates a response - Output- Computer makes a move, which appears on

your screen

What is quantum computing?

- Exploiting the strange phenomena in quantum

mechanics to process information - Quantum computers can be in a superposition of

several states, so you can process information in

parallel

Bit vs. Qubit

- Superposition of classical states, so you can

contain as many inputs as you want and process

in parallel!

Measurement problems?

- Quantum computing is probabilistic- we could run

exactly the same program twice and see different

results - But you can repeatedly initialize, run, and

measure

Thought Experiment

- Impossible task-- find a small X that has been

marked on one book in the Library of Congress in

less than five minutes - But what if there were several million parallel

Library of Congress and each one had a parallel

self? If you could coordinate with all of the

parallel selves, you might be successful.

Why Quantum Computing is a Big Deal

- Can solve enormous tasks in a reasonable amount

of time finding a needle in a haystack - True random number generation
- Implications for artificial intelligence?
- National security

More about National Security

- Our daily lives depend on encryption
- Encodes message so that they are useless to

anyone who doesnt know the cipher - Prevents eavesdroppers on mobile phone

conversations, protects information being

transferred over the network, etc. - Symmetric key scheme

Another kind of Encryption

- Banking, medical records, business records, and

government records often use RSA encryption tools - This relies on the difficulty of breaking a very

large number into two prime factors

Factors of a very large number!

Safe For now

- In 2009, computer scientists were able to crack

the primes for a 768-bit number over the span of

two years and using hundreds of computers - Many encryption keys are 1024 bits, so it would

even take 1000 times longer to crack! - However, quantum computers could use a process

called Shors algorithm to crack very large

encryption keys

Quantum Key Distribution (QKD)

- QKD depends on three properties
- Photon Polarization
- Heisenberg uncertainty principle
- No-cloning theorem

Photon Polarization

- Unpolarized (normal) photons can spin in all of

their directions at once - Can be polarized by passing through a filter
- Cant be re-polarized without losing information

Uncertainty Principle

- Some kinds of knowledge are fundamentally

inaccessible - For example, the more precisely you measure a

particles position the less precisely you can

know its momentum. - It is also impossible to know a photons spin in

two directions at once!

Quantum No-Cloning Theorem

- Suppose you can create multiple identical

properties of a quantum state - Then you can measure position in one state and

momentum in another - This violates the Heisenberg uncertainty

principle!

BB84 Protocol

- Alice chooses a random polarization and records

her result - Bob also chooses a random polarization and

records his result

BB84 Protocol

- At the end, Alice can read off what polarizing

filters she used and they can keep sets that

agree - This will give them a private code!

What if Eve was eavesdropping?

- Eve would have to randomly measure the photon to

obtain information. - Half of the time she will choose the wrong

filter. Then if Bob chooses the right filter, his

result will be random and might be different from

Alices - Bob and Alice can compare a small portion of

their code over the classical channel and see

whether Eve was eavesdropping

Problems with Quantum Encryption

- Noisy and imperfect equipment might make Bob and

Alices measurements disagree - Imperfect photon source helps Eve eavesdrop

Problems with Quantum Computation

- Quantum systems are very delicate
- Decoherence (interactions with the environment)

can quickly collapse the wavefunction

When will quantum computers be made?

- 1998- First three qubit computer
- 2012- Decoherence suppressed for 2 seconds at

room temperature - 2013- Decoherence suppressed for 39 minutes at

room temperature in an ensemble of 3 billion

qubits

Thank you for Listening

Tunneling

- Consider a ball rolling off into a valley, bound

on the other side by a higher hill. Classic

physics states that the ball cannot have

sufficient energy to roll over from the other

side of the higher hill unless an external

velocity is imparted on this ball, but according

to quantum tunneling, there is the minute

possibility that this ball will turn out to be

that one coincidence out of a million and DIG

THROUGH the hill instead of rolling over.

Black Hole Information Paradox

- The reason that this lost information is such a

major issue for quantum mechanics once again ties

into thermodynamics. In quantum mechanics,

information is related to the thermodynamic

concept of order. If information is lost, then

order is lost meaning that entropy (disorder)

is increased. This means that the black holes

would begin generating heat, rising up to

billions of billions of degrees in mere moments.

Though Leonard Susskind and others realized this

in the mid-1980s, they couldnt find the flaws in

Hawkings reasoning that would prove him wrong. - he redid some of his earlier calculations and

found that it was possible that, as an object

fell into a black hole, it would disturb the

black holes radiation field. The information

about the object could seep out, though probably

in mangled form, through the fluctuations in this

field. - it may be possible that all the information

within the black hole is also encoded in some

form on the surface area of the black hole.

Uncertainty Principle in Pictures

More Precise Position, Less Precise Momentum

Precisely determined momentum, unknown position

Quantum Entanglement- Spooky Action At A

Distance

- ?Particles can be connected, even across great

distances! - ?Example- laser beam fired through specific

crystal can cause individual photons to split

into pairs of entangled photons - When you measure the spin of particle A, you

determine the spin of particle B virtually

instantaneously!

Alternative View- Many Worlds Approach

- Wavefunction doesnt magically collapse upon

observation! - Instead, we start with a superposition
- After measuring, the superposition is still

there but the different branches can no longer

interact with each other - This is due to decoherence

Many-Worlds Interpretation

- Schrodingers cat is alive in one world and dead

in another - When you open the box you can say which world

you are in. You are either in world-1 or world-2,

but both the worlds exist.

Phenomena 1- Quantization

- In 1900 Max Planck started a revolution in

physics without realizing it - Blackbody- an object that perfectly absorbs and

emits radiation - Experimental data could be fit by assuming that

energy was quantized!

More Quantization

Electrons restricted to specific energy levels

More Quantization

- Energy
- Momentum/Velocity

What is light?

- Debate goes all the way back to Aristotle and

Democritus - Lots of evidence for light to be a wave

Light as a Particle

- More intense light doesnt lead to more intense

radiation - 1905- Einstein hypothesized that light may be

composed particle-like pieces (photons) - Existence of photons later confirmed (1923)

What about matter?

- Familiar with definition of matter as a

collection of particles (for example, a

baseball). - We have never observed baseballs diffracting

around corners

Double Slit Experiment

- Light produces interference patterns when passed

through a slit

Electrons can also act like a wave

- Interference builds up over time

Recap

- Momentum, energy can be quantized
- Light can act like a wave and a particle
- Matter can act like a group of particles and a

wave

Even Stranger- Double Slit Experiment Revisited

- If particle detectors are positioned at the slit,

the interference pattern will disappear - We cannot observe something acting as a particle

and wave at once

Quantum Mechanics in Pop Culture

New Age Religion

Obscure Math

Image Source Church of the Cosmos

We are immortal timeless beings of light in an

infinitely expanding omniverse filled with

intelligent life.