Transcript brandsen30Popx - Caltech High Energy Physics

Quantum Mechanics
and
Quantum Computation
Sarah Brandsen
“If quantum mechanics hasn’t
profoundly shocked you, you haven’t
understood it yet.”
-Niels Bohr
Outline
• What is Quantum Mechanics?
• Phenomena
– Quantization
– Wavefunctions and Schrodinger’s 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 PhysicsSchrodinger’s 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 Schrodinger’s 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 cat’s 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 don’t 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 doesn’t 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 Shor’s 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
• Can’t be re-polarized
without losing information
Uncertainty Principle
• Some kinds of knowledge are fundamentally
inaccessible
• For example, the more precisely you measure
a particle’s position; the less precisely you can
know its momentum.
• It is also impossible to know a photon’s 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 Alice’s
 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 Alice’s 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 couldn’t find the flaws in
Hawking’s 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 hole’s 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 doesn’t 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
• Schrodinger’s 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
doesn’t 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
Image Source: Church of the Cosmos
“We are immortal timeless beings of light
in an infinitely expanding omniverse filled
with intelligent life.”
Obscure Math