“ Anyone who can contemplate quantum mechanics without getting dizzy hasn ’ t understood it. ” Niels Bohr. The Quantum Information Revolution Paul Kwiat. DARPA. Kwiat’s Quantum Clan (2012) Graduate Students: Rebecca Holmes Aditya Sharma Trent Graham Brad Christensen
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“Anyone who can contemplate quantum mechanics without getting dizzy hasn’t understood it.”
Niels Bohr
Clan (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 Rhodes
Visit Prof: Hee Su Park
PostDoc:Jian Wang
Factoring
Simulating other quantum
systems (>30bits)
Ultimate control over
Error correction
“large” systems
Quantum
classical
Quantum
Quantum communciation
Information
Teleportation
Linking separated
quantum systems
(“q. network”)
Quantum cryptography
Secure key distribution
(even between
nonspeaking parties)
Fundamental physics
Entanglement
Decoherence
Quantum metrology
Measurements beyond
the classical limit
Noninvasive measurements
Measurements on quantum
systems
very small
very 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 above
wavelength
6.6 x 1034Js
frequency
Visible light
Power output: P = (# photons/sec) x Ephoton
How do we reconcile this notion that light comes in ‘packets’ with our view of an electromagnetic wave, e.g., from a laser??
Partially transmitting mirror
Power input
How many photons per second are emitted from a 1mW laser (l=635nm)?
3 x 1015 photons/sec =
3,000,000,000,000,000/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!!
A. Rose, J. Opt. Sci. Am. 43, 715 (1953)
Exposure time
But how do we *know* there’s only ONE photon…
A beamsplitter…
Photon only detected in one output.
Equally likely to be transmitted or reflected –cannot tell which.
"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.”
There is film in the camera!”
Quantum InterrogationThe problem…
Measure film absorber atom without exposing heating exciting it
Waves add up:
“Constructive interference”
Waves cancel:
“Destructive interference”
1675: Newton “proved” the light was made of “corpuscles”
1818: French Academy science contest
Judge Arago decided to actually do the experiment…
Conclusion (at the time): Light must be a wave, since particles don’t interfere!
Exposure time
Photons
?
beam
splitter
Optical Interferometers
MachZehnder: Michelson :
beam
splitter
mirror
There is film in the camera!”
Quantum InterrogationThe problem…
Measure film absorber atom without exposing heating exciting it
The solution…(Elitzur & Vaidman, 1993)Use dual waveparticle nature of quantum objects (“wavicles”)
Single photon always shows up at D1(complete destructive interference to D2)
Now place an absorbing object in one arm…
50% chance that photon is absorbed by object50% chance it isn’t 25% chance D2 fires “interactionfree measurement” of object
Quantum Cryptography = Quantum Key Distribution
Cryptography
KEY:
…010001010011101001…
XOR(Cipher,Key)
Message
XOR(Message,Key)
Cipher
EVE
ALICE
BOB
Cipher:
…0110010110100010…
Polarization: the oscillation direction of the light
property of each photon
can measure with polarizers, calcite, etc.
Prob(horizontally polarized photon pass horizontal polarizer): 1
Prob(horizontally polarized photon pass vertical polarizer): 0
Prob(diagonally pol. photon pass horizontal polarizer): 1/2
Prob(diagonally pol. photon pass vertical polarizer): 1/2
“Spontaneous
DownConversion”:
high energy parent photon can split into two daughter photons
(with same polarization)
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.
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!
Quantum Interrogation vs. Quantum Cryptography
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!
Source: Intel
The first solidstate transistor
(Bardeen, Brattain & Shockley, 1947)
“bit”“qubit”
0, 10101
Physical realization of qubits any 2 level system
2level atom: ge
spin1/2:
polarization: HV
All 2level systems are created equal, but some are more equal than others!
Quantum communication photons
Quantum storage atoms, spins
Scaleable circuits superconducting systems
“Quantum” phenomena
Superposition
Interference
Waveparticle duality
Intrinsic randomness in measurement
Entanglement
“Entanglement”, and the scaling that results, is the key to the power of quantum computing.
1
0
1
•
Classically
, information is stored in a bit register: a 3bit
register can store
one
number, from 0 – 7.
Quantum Mechanically, a register of 3 entangled qubits can store all of these numbers in superposition:
•
a

000
+ b

001
+ c

010
+ d

011
+ e

100
+ f

101
+ g

110
+ h

111
ñ
ñ
ñ
ñ
ñ
ñ
ñ
ñ
Result:
•
Classical:
one Nbit number


Quantum:
2
(all possible) Nbit numbers
N
register can simultaneously store
•
N.B.
:
A 300
qubit
2300 ~ 1090 numbers
1090 =
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
This is more than the total number of particles in the Universe!
Some important problems benefit from this exponential scaling, enabling solutions of otherwise insoluble problems.
A hard problem: factoring large integers:
For example, it is hard to factor 167,659
But an elementary school student can easily multiply389 x 431 = 167,659
This asymmetry in the difficulty of factoring vs. multiplying is the basis of public key encryption, on which everything from online transaction security to ensuring diplomatic secrecy depends.
Quantum Computing’s “killer app.”
Quantum algorithms enable one to factor numbers into their prime constituents MUCH faster:
The 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).
Atom in different energy states:
state labels
“”, “”
energy states:
atom in
state
atom in
state
atom
atom in
superposition state
shorthand “wave function”
representation
= +
Probability of measuring , P = 2
Probability of measuring , P= 2
rest + moving
0
0
0
0
1
Collective motion: the “quantum data bus”
state of motion
rest
0
0 + 1
0
0
1
Quantum Computing Explored
Sep 12 2001 @ 08:10
American computer scientists are studying the possibility to build a super fast computer based on quantum physics.
Technology requirements
Essential Dichotomy
Need 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.
Quantum
Computation
The expected
The unlikely – impossible?
Difficulty/Complexity
The known
Quantum
Measurement
Quantum
Communication
0 5 10 ~15 20? 25??
Time (years)
Quantum
Widgets
Quantum
Engineered Photocells?
Quantum
Sensors?
The as yet unimagined!!!
Quantum
Games & Toys
control electrodes
Quantum factoring and cryptography
# of instructions
Classical ~ eAL
~ 1017 instructions: 8 months
Quantum~ L3
~ 109 operations: seconds
RSA129
# of bits, L, factored