t understood it Niels Bohr The Quantum Information Revolution Paul Kwiat DARPA Kwiats Quantum Clan 2012 Graduate Students Rebecca Holmes Aditya Sharma ID: 619245
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Slide1
“
Anyone who can contemplate quantum mechanics without getting dizzy hasn
’
t understood it.
”
--Niels BohrSlide2
The Quantum Information Revolution Paul Kwiat
DARPASlide3
Kwiat’s
QuantumClan (2012)Graduate Students:
Rebecca Holmes
Aditya Sharma
Trent Graham Brad Christensen
Kevin Zielnicki
Mike Wayne
Courtney Byard
Undergraduates: Daniel Kumor
David
Schmid Jia Jun (“JJ”) Wong
Cory
Alford Joseph Nash David RhodesVisit Prof: Hee Su ParkPost-Doc: Jian WangSlide4
A New Science!
Quantum
Mechanics
Information
Science
Quantum Information Science
20th Century
21st Century
Slide5
Quantum
Information
Fundamental physics
Decoherence
Quantum
classical
Entanglement
Ultimate control over
“
large
”
systems
Quantum metrology
Measurements beyond
the classical limit
Non-invasive measurements
Measurements on quantum
systems
Quantum cryptography
Secure key distribution
(even between
non-speaking parties)
Quantum computation
Factoring
Simulating other quantum
systems (>30bits)
Error correction
Quantum communciation
Teleportation
Linking separated
quantum systems
(
“
q. network
”
)Slide6
Quantum Metrology
Quantum Computing
Quantum CryptographySlide7
“
Things should be made as simple as possible, but not any simpler.”Slide8
What
I do…Unravel the mysteries of the universe…
Quantum Optics
Light
???Slide9
Quantum…
very smallvery big (e.g., “quantum leap”)
an unsplittable parcel/bundle of energy
a cool buzzword to get more funding, more papers, more people at your Sat. am physics lecture, etc.all of the aboveSlide10
1905: Einstein made a ‘quantum leap’ and proposed that light was really made of particles with tiny energy given by
E = h f = h c/l
frequency
6.6 x 10
-34
J-s
wavelengthSlide11
Power input
Partially transmitting mirror
How many photons per second are emitted from a
1-mW
laser (
l
=635nm
)?
How do we reconcile this notion that light comes in
‘
packets
’
with our view of an electromagnetic wave, e.g., from a laser??
Power output: P = (# photons/sec) x E
photon
Visible light
Physics 214: Lect. 7
Example
:
“Counting photons”Slide12
1
mW red laser3 x 1015 photons/sec =
This is an incredibly huge number – your eye basically cannot resolve this many individual photons (though the rods can detect single photons!
). And
you MAY be able to see just one photon!!
3,000,000,000,000,000/sec
Slide13
Formation of Optical Images
For large light intensities
, image formation by an optical system can be described by classical optics.
Exposure time
However,
for very low light intensities
, one can see the statistical and random nature of image formation.
Use an extremely sensitive CCD camera that can detect single photons.
A. Rose, J. Opt. Sci. Am. 43, 715 (1953)Slide14
"God does not play
dice with the universe."
“It seems to me that the idea of a personal God is an anthropological concept which I cannot take seriously.
”
Photon only detected in one output.
Equally likely to be transmitted or reflected
–
cannot tell which.
A
beamsplitter…
But how do we *know* there’s only ONE photon…
Quantum random-number generator!completely unpredictablepatentedcommercially available“0”“1”Slide15
“
The important thing is not to stop questioning.” -A. EinsteinSlide16
Quantum
Interrogation
“
Yes, yes, already, Warren! … There
is film in the camera!”
The problem…
Measure
-film -absorber
-atom without -exposing -heating
-exciting itSlide17
WHY was Einstein’s 1905 proposal that light was made of particles such a profound leap
that almost no one believed him?Because everyone KNEW that light was really waves.One of the strangest features of QM: all particles can behave like waves…Slide18
Interference of
waves (e.g., water, sound, …)Slide19
Superposition (adding together)
of wavesWaves add up:“Constructive interference”
Waves cancel:
“Destructive interference”Slide20
Light:
Particle or Wave?
1675: Newton
“
proved” the light was made of “corpuscles”
1818: French Academy science contest
Fresnel proposed interference of light.Judge Poisson
knew light was made of particles: “Fresnel’s ideas ridiculous” If Fresnel ideas were correct, one would see a bright spot in the middle of the shadow of a disk.Slide21
Judge Arago decided to actually do the experiment…
Conclusion (at the time):
Light
must be a wave, since particles don’t interfere!
Only, now we know
that they must!Slide22
Single-Photon
Interference:Question: what if we reduce the source intensity so that at most one particle (photon) is in the apparatus at a time?
Exposure time
Answer:
Just like in the
“
optical image formation
”
, given enough time, the
classical interference pattern
will gradually build up from a huge # of seemingly random
“events”!
Photons
?Slide23
Optical Interferometers
Interference arises when there are two (or more) ways for something to happen, e.g.,
sound from two speakers reaching your ear.
An interferometer is a device using mirrors and “beam splitters” (half light is transmitted, half is reflected) to give two separate paths for light to get from the source
to the detector.
Two common types: Mach-Zehnder:
Michelson :
mirror
beam-
splitter
beam-
splitter
mirrorSlide24
Quantum
Interrogation
“
Yes, yes, already, Warren! … There
is film in the camera!”
The problem…
Measure
-film -absorber
-atom without -exposing -heating
-exciting itSlide25
The solution…
(Elitzur & Vaidman
, 1993)Use
dual wave-particle nature of quantum objects (“wavicles”)
Single photon always shows up at D1
(complete destructive interference to D2)Slide26
Now place an absorbing object in one arm…
50% chance that photon is absorbed by object
50% chance it isn
’t 25% chance D2 fires
“interaction-free measurement
” of objectSlide27
Quantum Interrogation
Optimizing
reflectivities
50% efficiencyBy combining these techniques with the
“quantum Zeno effect” (making repeated very weak interactions), the efficiency can in principle be pushed to 100%: no photons absorbed by the absorbing object!
[85% demonstrated to date]
Imaging semi-transparent objects does not readily yield a gray-
scaleSlide28
Quantum Metrology
Quantum Computing
Quantum Cryptography
Wpdrval
L&wz;xcuymnzx
Slide29
Cryptography:
Make messages so that only the intended recipient can understand them…public key encryption: Standard, but not provably secure; relies on difficulty of factoring (e.g., 15 = 3x5)
secret key encryption: PROVABLY secure as long as no one else has the key
the key is never reused
Quantum Cryptography = Quantum Key DistributionSlide30
ALICE
BOB
Cipher:
…0110010110100010…
XOR(Cipher,Key)
Message
EVE
KEY:
…010001010011101001…
Quantum Cryptography
Cryptography
XOR(Message,Key)
CipherSlide31
Quantum Cryptography:
Use a different property of light– polarization!Prob(horizontally polarized photon pass horizontal polarizer): 1
Polarization: --the oscillation direction of the light--property of each photon
--can measure with polarizers, calcite, etc.
Prob(horizontally polarized photon pass vertical polarizer): 0
Prob
(diagonally pol. photon pass horizontal polarizer): 1/2
Prob
(diagonally pol. photon pass vertical polarizer): 1/2Slide32
How to Make
“Entangled” Coins
We don’t know WHICH crystal created the pair of photons, but we know they both came from the
same
crystal
they
MUST have the same polarization.
“Spontaneous
DownConversion
”:
high energy parent photon can split into two daughter photons(with same polarization)Slide33
Entangled-Photon Quantum Cryptography
Alice & Bob randomly measure polarization in the (HV) or the (45 45) basis.
Discuss via a
“
public channel
”
which bases they used,
but not the results. Discard cases (50%) where they used different bases
uncorrelated results. Keep cases where they used the same basis perfectly correlated results! Define H “0
”
45, V “1”
45. They now share a secret key.Slide34
Eve cannot
“tap” the line
photons that don’t make it to Bob are not part of the key
Eve cannot “clone” the photon
forbidden by basic quantum mechanics
Measurements by Eve necessarily have a chance (25
%) to disturb the quantum state
Alice and Bob can detect errors in the key!
If the bit error rate is too high, they simply discard the key. No message is ever compromised.What about Eavesdropping?Slide35
Current Free-Space QKD Distance Record: 144
km between LaPalma and Tenerife
Last week news item: they used the entangled photons to teleport the state of a photon between the islands – world distance record for quantum teleportation!Slide36
QKD Goes Commercial…Slide37
Since we can seemingly
“see” without “
looking” using quantum interrogation, does this mean an eavesdropper could use it to defeat quantum cryptography?
No! It turns out that even making the gentlest measurement possible, if the eavesdropper gains any information, she disturbs the state.Or if she is so gentle so as not to disturb the state, then she gets no information.Quantum key distribution is secure against any
attack allowed by the laws of physics!
Quantum Interrogation vs.
Quantum CryptographySlide38
Imagination is more important than knowledgeSlide39Slide40
Source: Intel
Moore
’
s LawSlide41
The first solid-state transistor
(Bardeen, Brattain & Shockley, 1947)Slide42
INTEL
Pentium 4
transistor
The Ant and
the Pentium
~100 million transistors
Size of an atom
~ 0.1nmSlide43
Superposition
Interference
Wave-particle duality
Intrinsic randomness in measurement
Entanglement
2-level atom
:
ge
spin-1/2:
polarization:
HV
Binary digit Quantum bit “bit” “qubit” 0, 1 0101
Physical realization of qubits
any 2 level system
All 2-level systems are created equal, but some are more equal than others!
Quantum communication
photons
Quantum storage
atoms, spins
Scaleable
circuits
superconducting
systems
“
Quantum
”
phenomenaSlide44
“
Entanglement”, and the scaling that results, is the key to the power of quantum computing.
•
Classically
, information is stored in a bit register: a 3-bit
register can store
one
number, from 0 – 7.
•
a
|
000
ñ
+ b
|
001
ñ
+ c
|
010
ñ
+ d
|
011
ñ
+ e
|
100
ñ
+ f
|
101
ñ
+ g
|
110
ñ
+ h
|
111
ñ
•
Result:
--
Classical:
one N-bit number
--
Quantum:
2
N
(all possible) N-bit numbers
•
N.B.
:
A 300-
qubit
register can simultaneously store
2
300
~ 10
90
numbers
1
0
1
Quantum Mechanically
, a register of 3 entangled
qubits
can store all of these numbers in superposition:Slide45
That’s a BIG number
1090
=
This is more than the total number of particles in the Universe!
1,000,000,000,000,000,000, 000,000,000,000,000,000
, 000,000,000,000,000,000
, 000,000,000,000,000,000, 000,000,000,000,000,000
Some important problems benefit from this exponential scaling, enabling solutions of otherwise insoluble problems. Slide46
A hard problem: factoring large integers
:
For example, it is hard to factor 167,659
But an elementary school student can easily multiply 389 x 431 = 167,659
This asymmetry in the difficulty of factoring vs. multiplying is the basis of public key encryption, on which everything from on-line transaction security to ensuring diplomatic secrecy depends.Slide47
Quantum Computing
’s “killer app.”
RSA
digitsPC(1 GHz)Blue Waters
(10PF)Quantum Computer (1 GHz)
1294 months1 sec
10 sec225300,000 yr
12 days100 sec3001016 yr
(>> universe)20 million yr200 secThe difficulty (impossibility) of factoring large numbers (and the ease of creating a large number from its factors) is the basis of public key encryption (which nearly everyone uses for secure transmission today). Quantum algorithms enable one to factor numbers into their prime constituents MUCH faster:Slide48
state labels
“
”, “ ”
Atom in different energy states:
atom
energy states:
atom in
state
atom in
state
atom in
superposition state
shorthand
“
wave function
”
representation
=
+
Probability of measuring , P
= |
|
2
Probability of measuring , P
= |
|
2Slide49
|0
|0
+ |1
|0
|0
|1
|rest
state of motion
Collective motion: the
“
quantum data bus
”
laser
|0
|0
|0
|0
|1
|rest + |movingSlide50
Science News
Quantum Computing ExploredSep 12 2001 @ 08:10
American computer scientists are studying the possibility to build a super fast computer based on quantum physics. Slide51
Technology requirements
Set of qubits isolated from environment.
“Quantum information bus” to connect qubits.
Reliable read-out method.
Essential DichotomyNeed WEAK coupling to environment to avoid decoherence, but you also need STRONG coupling to at least some external modes in order to ensure high speed and reliability.
Why it might not work…Slide52
Quantum Information Timeline
0 5 10 ~15 20? 25??
Time (years)
Difficulty/Complexity
Quantum
Measurement
Quantum
Communication
The known
Quantum
Computation
The expected
The unlikely – impossible?
Quantum
Sensors?
The as yet unimagined!!!
Quantum
Engineered Photocells?
Quantum
Widgets
Quantum
Games & ToysSlide53
“
Why is it that nobody understands me, and everybody likes me?” – A.E.Slide54
Quantum Imaging
No object:
photon leaves
45˚-polarized
no counts at D
2
Object blocks beam:
photon leaves
H-polarized counts at D2
Scan object through
beam waist micron resolution Slide55
Reduced Absorption
“Imaging”
Detecting the object with less than one photon!Slide56
Interconnected multi-trap structure
Route ions by controlling electrode potentials
Processor sympathetically cooled
No individual optical addressing during two-qubit gates
(can do gates in strong trap fast)
One-qubit gates in subtrapReadout in subtrap
Multiplexed Ion Trap Architecture
control electrodesSlide57
Quantum factoring and cryptography
Classical
~ e
AL
# of instructions
# of bits, L, factored
Quantum
~
L
3
RSA129
~ 10
9
operations:
seconds
~ 10
17
instructions:
8 months
the RSA cryptosystem:
polynomial
work to encrypt/decrypt
exponential
work to break = factoring
BUT quantum factoring is only
polynomial work
“
latency
”
: will information encrypted today be secure against future quantum computers?Slide58
Quantum Mechanics and Information Science were two of the most important and revolutionary developments of the 20th century:
Quantum Mechanics
changed the way we think about the physical world and enabled a wealth of new technology, including lasers, solid state electronics--the foundations of much of what we identify with modern life.
Information Science changed the way we think about “thinking.” Digital information processing is ubiquitous in communication, entertainment, commerce, manufacturing, science…And its implementation has depended on the devices of quantum mechanics.