“Anyone who can contemplate quantum mechanics without getting dizzy hasn’t understood it.”

--Niels Bohr

The Quantum Information Revolution

Paul Kwiat

Kwiat’s QuantumClan (2012)Graduate Students:

Rebecca HolmesAditya SharmaTrent GrahamBrad ChristensenKevin ZielnickiMike WayneCourtney Byard

Undergraduates:Daniel KumorDavid SchmidJia Jun (“JJ”) WongCory AlfordJoseph NashDavid Rhodes

Visit Prof: Hee Su ParkPost-Doc: Jian Wang

A New Science!

QuantumMechanics

InformationScience

Quantum Information Science

20th Century

21st Century

Quantum Information

Fundamental physics

Decoherence

Quantum classical

Entanglement

Ultimate control over “large” systems

Quantum metrologyMeasurements beyond

the classical limitNon-invasive measurementsMeasurements on quantum

systems

Quantum cryptographySecure key distribution (even between

non-speaking parties)

Quantum computationFactoringSimulating other quantum

systems (>30bits)Error correction

Quantum communciationTeleportationLinking separated

quantum systems (“q. network”)

Quantum Metrology

Quantum Computing

Quantum Cryptography

“Things should be made as simple as possible, but not any simpler.”

What I do…

Unravel the mysteries of the universe…

Quantum Optics

Light???

Quantum…a. very smallb. very big (e.g., “quantum leap”)c. an unsplittable parcel/bundle

of energyd. a cool buzzword to get more

funding, more papers, more people at your Sat. am physics lecture, etc.

e. all of the above

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

frequency6.6 x 10-34J-s wavelengt

h

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??

photonhcEl

1240eV-nm 2eV635 nm

Power output: P = (# photons/sec) x Ephoton

315 1

-19

10 J 1eV 1photon(# photons/sec) 3.1 10 ss 1.6 10 J 2eVphoton

PE

Visible light

Physics 214: Lect. 7Example: “Counting photons”

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

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)

"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 unpredictable• patented• commercially available

“0”

“1”

“The important thing is not to stop questioning.”

-A. Einstein

Quantum Interrogation

“Yes, yes, already, Warren! …

There is film in the camera!”

The problem…

Measure -film -absorber-atom

without-exposing-heating-exciting it

WHY was Einstein’s 1905 proposal that light was made of particles such a profound leapthat 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…

Interference of waves (e.g., water, sound, …)

Superposition (adding together) of waves

Waves add up:“Constructive interference”

Waves cancel:“Destructive interference”

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.

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!

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?

Expo

sure

tim

e 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

?

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 mirror

Quantum Interrogation

“Yes, yes, already, Warren! …

There is film in the camera!”

The problem…

Measure -film -absorber-atom

without-exposing-heating-exciting it

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)

Now place an absorbing object in one arm…

50% chance that photon is absorbed by object50% chance it isn’t 25% chance D2 fires

“interaction-free measurement” of object

Quantum Interrogation

• Optimizing reflectivities 50% efficiency• By 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-scale

Quantum Metrology

Quantum Computing

Quantum Cryptography

Wpdrval

L&wz;xcuymnzx

Cryptography: Make messages so that only the intended recipient can understand them…1. public key encryption: Standard,

but not provably secure; relies on difficulty of factoring (e.g., 15 = 3x5)

2. secret key encryption: PROVABLY secure as long as a. no one else has the keyb. the key is never reusedQuantum Cryptography = Quantum Key Distribution

ALICE BOB

Cipher:…0110010110100010…

XOR(Cipher,Key)

Message

EVE

KEY:…010001010011101001…

Quantum CryptographyCryptography

XOR(Message,Key)

Cipher

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): 0Prob(diagonally pol. photon pass horizontal polarizer): 1/2Prob(diagonally pol. photon pass vertical polarizer): 1/2

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)

• 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?

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!

QKD Goes Commercial…

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 Cryptography

Imagination is more important than

knowledge

Source: Intel

Moore’s Law

The first solid-state transistor(Bardeen, Brattain & Shockley, 1947)

INTEL Pentium 4 transistor

The Ant and the Pentium~100 million transistors

Size of an atom~ 0.1nm

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

0101Physical realization of qubits any 2 level system

All 2-level systems are created equal, but some are more equal than others!Quantum communication photonsQuantum storage atoms, spinsScaleable circuits superconducting systems

“Quantum” phenomena

“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-bitregister can store one number, from 0 – 7.•

a|000 + b|001+ c|010 + d|011 + e|100 + f|101 + g|110 + h|111

• Result:-- Classical: one N-bit number-- Quantum: 2N (all possible) N-bit numbers

•N.B.: A 300-qubit register can simultaneously store2300 ~ 1090 numbers

101

Quantum Mechanically, a register of 3 entangled qubits can store all of these numbers in superposition:

That’s a BIG number1090 =

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.

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 = 167,659This 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.

Quantum Computing’s “killer app.”

RSA digits PC(1 GHz)

Blue Waters(10PF)

Quantum Computer (1 GHz)

129 4 months 1 sec 10 sec

225 300,000 yr 12 days 100 sec

300 1016 yr(>>

universe)

20 million yr

200 sec

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).

Quantum algorithms enable one to factor numbers into their prime constituents MUCH faster:

state labels “ ”, “ ”

Atom in different energy states:

atom

energy states: atom instate

atom instate

atom insuperposition state shorthand “wave function”

representation

= +

Probability of measuring , P = ||2

Probability of measuring , P = ||2

|0 |0 + |1 |0 |0 |1

|rest

state of motion

Collective motion: the “quantum data bus”

laser

|0 |0 |0 |0 |1

|rest + |moving

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.

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…

Quantum Information Timeline

0 5 10 ~15 20? 25??Time (years)

Diff

icul

ty/C

ompl

exity

QuantumMeasurementQuantum

Communication

The known

QuantumComputation

The expected

The unlikely – impossible?

QuantumSensors?

The as yet unimagined!!!

QuantumEngineered Photocells?

QuantumWidgets

QuantumGames & Toys

“Why is it that nobody understands me, and everybody likes me?”

– A.E.

• 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 subtrap• Readout in subtrap

Multiplexed Ion Trap Architecture

control electrodes

Quantum factoring and cryptographyClassical ~ eAL

# of instructions

# of bits, L, factored

Quantum~ L3

RSA129

~ 109 operations: seconds

~ 1017 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?