spookytechnology and society - stanford university · nanotechnology is the creation of functional...

(C) Charles Tahan, 21 May 2008, Stanford Computer Systems EE380 Colloquium,

Available at http://www.tahan.com/charlie/1

Thoughts on the status and implications of

quantum information science and technology

Spookytechnology

and Society

Charles Tahan, PhD, [email protected]

Office address: DARPA – Microsystems Technology Office

3701 N. Fairfax Dr., Arlington, VA 22203 : Room 508

[email protected]

Office phone: 571-218-4536

http://www.tahan.com/charlie/



Who is this guy?

QuickTime™ and a decompressor

are needed to see this picture.



Technical consultant to DARPA on quantum

information S&T programs

Employee of S&T consulting division of

---- ----- -------- (a large gov.

contractor)

Condensed matter physicist

PhD, U. Wisconsin-Madison ‘05

NSF Distinguished International Postdoctoral Research Fellow‘05-’07 (Cambridge University-UK, U. Melbourne-AU, U. Tokyo-JP)

As of Oct 07



Silicon and GaAs quantum computing



Spintronics

Quantum Many-Body Physics

Quantum photonics: systems and devices

BS, Physics and Comp. Sci. ‘00

The opinions I share today are completely my own and in no

way represent the views of my employer or clients.



Not a talk about quantum computers

QuantumOverviewTechnologyQuantum InformationDevices

“Nanotechnology and Society”Where I’m coming fromScience and Tech StudiesDefining “nano”Sociology, Government, Historical Context

ContextWhat I was working onIntro to Quantum Information

SpookytechMy proposalMotivation and JustificationReactionAlternativesDiscussion

Preparing for the futureWrap-upCreating itCompetition6 months on

PhysicsQuantum DevicesCond-matQ.Info

ExamplesSilicon Quantum ComputingQuantum MetrologySolid Light



A few words about DARPA and what I do…

“DARPA’s original mission, established in 1958, was to prevent technological surprise like the launch of Sputnik.”

• Project-based (3-5 years), program manager driven

– ~140 technical program managers (3-5 year terms)

– ~20 senior managers

– ~120 support staff

– the rest contractors (technical, programmatic, support)

• High tech - but no operational or political roles

• Long, cool history (check it out)

• “DARPA hard”

• I won’t talk about anything going on at DARPA



Revolutions

~5,000 - 3,000 BC - First great technological revolutiong• the “irrigation society” -Drucker

~1750 AD - Second great tech revolutionMajor RevolutionsMajor RevolutionsMajor RevolutionsMajor Revolutions after 1750 (start date)

the industrial revolution (1771)

the age of steam and railways (1829)

the age of steel, electricity and heavy engineering (1875)

the age of oil, the automobile and mass production (1908)

the first quantum revolution (1945)

the age of information and telecommunications (1971)

the age of bio-engineering (1980)?

the second industrial revolution - nano (2005)?

the second quantum revolution (2015)?the second quantum revolution (2015)?the second quantum revolution (2015)?the second quantum revolution (2015)?

the age of machine-phase nanotechnology (2030-50)?

Incre

asin

g r

ate

of

innovation

Spooky?



The new quantum story

1. Recent ability to trap/create/control single quanta of nature (electrons, photons, atoms, plasmons,

magnons,…)

� Verify our interpretation of QM

� Technology

2. Re-visiting less-understood and largely ignored aspects of quantum theory

� New approach to many problems

� Non-locality, superposition, measurement

� Physical foundation for information theory and computation

3. “Spookytechnology” as a unifying term

4. What I’m interested in today: how this revolution unfolds,

how we define it, how we guide it to the public and policy makers, how we prepare for it



National Nanotechnology Initiative and Society

• This year research on the societal implications of nanotechnology accounts for nearly 10% of direct federal funding on nanotechnology in the United States: 80% of that on environmental and toxicological effects and the remaining on broader sociological studies. (Mihail Roco, 2003)

• Purpose?

– GMO, education, clever

• “Nanotechnology and Society” as keyword



Nanotechnology and Society

• 2005: Opportunity to teach my own class on “nanotechnology and society” as a 5th-year grad student

– Course development with profs from Sociology, Public Affairs, History of Science, Engineering

– Negatives: this helps your science career how?

– Advantages - totally different community, nanoethics, nanotechnology task force in UK

• First question: What is nanotechnology?

– Totally ambiguous

C. TAHAN, R. LEUNG, G.M. ZENNER, K.D. ELLISON, W.C. CRONE, and C.A. MILLER, “Nanotechnology and Society: A discussion-based undergraduate course,” Am.J. Phys. 74, 443 (April 2006)



QuickTime™ and aTIFF (Uncompressed) decompressor


Size and Scale: Factors of 1000

mete

rs

100

10-3m

illimete

rs

10-6m

icro

mete

rs


are needed to see this picture.10-9

nan

om

ete

rs

.

.

Hair: ~40 microns

.

1 nm = 10 Hydrogen atoms:

DNA:

1-2 nm diameter

Virus: 3-50 nm

Bacteria: 3-5 microns

MEMS

Retinal Implant





Defining Nanotechnology

NSF/NNI’s def:

Nanotechnology is the creation of functional materials, devices, and

systems through control of matter on the nanometer length scale,

exploiting novel phenomena and properties (physical, chemical,

biological) present only at that length scale (Roco).





c. 1960History

Feynman:

• miniaturization

• info. storage

• precision chemistry

• tiny machines

making tinier

machines

c. 1987 • “nanotech”popularized

• idea of molecular self-assemblars

c. 1990• S&T started to

catch up





c. 1974• “nanotechnology”coined for first time



Quantum (as in

quantized, not q.info)Chemical Biological

New properties at nanoscale





Completely different physical behavior than bulk.



More surface area per volume. More reactive.

Nanoparticles can cross the blood brain barrier. Microparticles can’t

Nanoparticles create real toxicological concerns.



Nanotech: Vision vs. Reality

C. TAHAN, “Identifying Nanotechnology in Society,” Chapter in Advances in Computers, edited by Marvin Zelkowitz (Elsevier, 2007). arxiv.org/abs/physics/0612080



My bipolar view of the

term “nanotechnology”

C. TAHAN, “The Nanotechnology R(evolution),” Chapter in Nanoethics: Examining the Societal Impact of Nanotechnology, edited by Fritz Allhoff, Patrick Lin, James Moor, and John Weckert (John Wiley & Sons, 2007), arxiv.org/physics/0612080

• Umbrella term

• Advanced materials

• GMR/CMR

• Bio

• Truth: Length scale effects

• New space race - funding

• Molecular nano-machines

• Self-assembly, self-replication

• “Machine-phase nanotechnology

• Grey goo



My definition for nano (focus on risk)

Nanotechnology, at present, is nanoparticles and

nanomaterials that contain nanoparticles. Nanoparticles are defined as objects or devices with at least two

dimensions in the nanoscale regime (typically under 10 nm) that exhibit new properties, physical, chemical, or

biological, or change the properties of a bulk material,due to their size. Nanotechnology of the future will include

atom-by-atom or molecule-by-molecule built active

devices.

C. TAHAN, “Identifying Nanotechnology in Society,” Chapter in Advances in Computers, edited by Marvin Zelkowitz (Elsevier, 2007). arxiv.org/abs/physics/0612080

C. TAHAN, “The Nanotechnology R(evolution),” Chapter in Nanoethics: Examining the Societal Impact of Nanotechnology, edited by Fritz Allhoff, Patrick Lin, James Moor, and John Weckert (John Wiley & Sons, 2007), arxiv.org/physics/0612080



Nanotechnology in whole

• Great uniting force for physical sciences at a practical level

• But threats too

• Nanotechnology has become a marketing term to

encompass and drive the belief that more funding is needed in the physical sciences to maintain economic, scientific,

and military advantage over international competition.

• What makes nano exciting to a STS person?

– Sociology of the mess

– The actual science, compartmentalized

– Risk dealt with

– Other than that?



Not a talk about quantum computers










What I was working on…

• Silicon nanodevices for quantum computing and spintronics

• Quantum information, a real revolution

– Thinking, language, as well

as application

• These nano STS people are really missing the boat!

2 coupled electron spins

in two quantum dots

100 nm

SET island

Single spin qubit readout

C. TAHAN, PhD Thesis (2005),

“Silicon in the quantum limit:

Quantum computing and spintronics

in silicon heterostructures”



Quantum Computers, the extreme “advanced quantum technology”

• 1st generation quantum technologies

– Quantum physics circa 1925

– Dual wave-particle like nature of matter - interference

– Quantization of particles (photons!)

– Electron waves in a semiconductor crystal

– Bulk systems

• Quantum-designed technologies: 1940s

– Atom bomb

– Transistor

– Laser

– Nuclear magnetic resonance (MRI)

• “New” quantum– Superposition

– Entanglement

– Coherence/Decoherence

– Measurement

– Quantum many-body effects

• 2nd generation quantum technologies

– Quantum communication (quantum key distribution to quantum repeaters)

– Quantum metrology, lithography, imaging – using entanglement for sub-wavelength resolution imaging/writing

– Specialized devices, based on, eg, EIT, slow light, BEC, etc.

– Quantum simulators (materials, drugs, …)

– Quantum computers (specialized to universal)

By 1925 there was a solidified interpretation of quantum mechanics that lead people to connect the mathematics to experience.

Dowling and Milburn got here first,

Proc. Royal Society



Peter ShorR. Feynman

Charles

Bennett

DavidDeutsch

• Simulate a quantum

system with another

quantum system?

1982

• First quantum algorithm

• Quantum teleportation

1993/1992

• Code breaking

Q.algorithm

• Quantum Error

Correction possible

1994-5

QC as intro to Quantum Information

“ok to get a

phd in this

stuff”



=

0

10

=

1

01Qubit:

“off” “on”

±=

±=±

1

1

2

1

2

10

“off AND on”

Quantum superposition

Multiple qubits:

[ ]180

1

0

0

1

0

0

1

1

00

1

01

0

1

1

0

0

1

010

×=

⊗

=

⊗

=

⊗

⊗

=⊗⊗

dimensional Hilbert space

Quantum Superposition and Formalism

3 qubits

2nHilbert space

for n qubits



Unentangled

(|0⟩⟩⟩⟩ + |1⟩⟩⟩⟩)××××(|0⟩⟩⟩⟩ + |1⟩⟩⟩⟩)

qubit 1

|0⟩⟩⟩⟩××××(|0⟩⟩⟩⟩ + |1⟩⟩⟩⟩) (prob. 0.5)

|1⟩⟩⟩⟩××××(|0⟩⟩⟩⟩ + |1⟩⟩⟩⟩) (prob. 0.5)

qubit 2

|00⟩⟩⟩⟩ (pr. 0.25) |01⟩⟩⟩⟩ (pr. 0.25) |10⟩⟩⟩⟩ (pr. 0.25) |11⟩⟩⟩⟩ (pr. 0.25)

Entangled

|01⟩⟩⟩⟩ + |10⟩⟩⟩⟩

qubit 1

|01⟩⟩⟩⟩ (pr. 0.5)

|10⟩⟩⟩⟩ (pr. 0.5)

Measurement of qubit 1 fixes

state of qubit 2.

Quantum Entanglement“Spooky action at a

distance”



The graph that says it all re: QC

1

1,00010010

1,000,000

1,000,000,000

10.10.010.0010.00010.00001

1000 times more classical

computing power









Shor

’ s quantum algorithm

100

PC

s (

c.

20

03)

100

,000

PC

s (

c.

20

03)

Number to factor (arbitrary units)

Tim

e t

o f

ac

tor

(arb

itra

ry u

nit

s)

Ru

n T

ime (

arb

itra

ry u

nit

s)

Problem Size (arbitrary units)

Van Meter, Thesis, 2008

Best

Cla

ssic

al A

lgo

rith

m



Unifying Language

• Inside Physics

– Condensed Matter

– AMO

– Information Theory

– High Energy Physics?

• Physics and Computer Science

– Information theory

• Mathematics

• Engineering

Quantum mechanics

courses that haven’t

changed really since the

1920s are being

rewritten.



Introducing Spookytech










MY PROPOSAL

• Fall 2008: “Spookytechnology and Society”

• My Goals:– Use the history of nanotech as a guide

– Start discussion on educational and societal issues in physics community

– Bridge the gap with science and tech studies community

– Propose new terminology and definition• Controversial

• Broader definition than just QC or QI

• “Quantum” overused

• Avoid ambiguous definition of field by outside (scifi, pop-sci)

– Cocktail party cool: Spookytechnology is technology based on the spooky properties of quantum physics



On being selectively ridiculous



My name and definition

spookytechnology encompasses all functional devices, systems, and materials whose utility relies in whole or in part on higher order quantum properties of matter and energy that have no counterpart in the classical world. These purely quantum traits may include superposition, entanglement, decoherence (along with the quantumaspects of measurement and error correction) or new behavior that emerges in engineered many-body systems.

"spukhafte Fernwirkung"

C. TAHAN, “Spookytechnology and Society,” (12 October 2007),

http://arxiv.org/abs/0710.2537



Nano vs. Spooky

• Spookytech still in inception phase - has not entered public conciousness

• No environmental implication

• Spookytech is really a new paradigm shift, whereas nano is more a loose confederation - or a practical paradigm

• Spookytech has a language founded on quantum optics (discrete QM) and information theory



Immediate community reaction







Immediate community reaction

1. Reminds me of casper the ghost.2. “Not rational”3. “We don’t want to scare

people/pseudoscience.”4. “quantum” is still sexy5. “Too anthropomorphic” David

Deutsch, Oxford Press6. Sounds like “pooh”7. Physicists don’t like “cute

words.” - P.Ball, Nature



Rational? Why not “meter-technology”?

Makes about as much sense as nano-technology when you think about it.

But making sense is not the point of most terms.



“It’s scary/it will lead to pseudo-

science”







Alternatives

• Quantum Technology

• 2nd Generation Quantum Technology

• Quantum Information Technology– Quinfotechnology

– QIT

• Quantum coherent technology

• Quantum entanglement-based technology

• Quantronics

Still sexy after all these years



My name and definition

spookytechnology encompasses all functional devices, systems, and materials whose utility relies in whole or in part on higher order quantum properties of matter and energy that have no counterpart in the classical world. These purely quantum traits may include superposition, entanglement, decoherence (along with the quantumaspects of measurement and error correction) or new behavior that emerges in engineered many-body systems.

"spukhafte Fernwirkung"

C. TAHAN, “Spookytechnology and Society,” (12 October 2007),

http://arxiv.org/abs/0710.2537

Quantum … technology



Examples of spookytech










• What we need:– Universal set of gates

– Good, scalable qubit

– Fast readout (measurement) of qubit

– Fast initialization / source of new qubits

– Quantum Error Correction

– Flying qubits

Quantum Algorithms /Computer Science,Math

Example: A Quantum Computer


in two quantum dots



Silicon towards quantum

• Silicon may be most studied material in history (but largely from an engineering perspective)

• Currently at 45 nm node

• Two ways to get to quantum: cold vs. small

• Quantum at room temperature

• Quantum at 10 milli-Kelvin


in two quantum dots

10 nm

E-beam lithography



Other promising quantum computing architectures

Superconducting qubits

Ion traps

Cold atom optical lattices

Photons and non-

linear optics

Electrons floating on liquid Helium



Spin relaxation times of electron spin in silicon

qubit

The longer thecoherence time of a

qubit, the less quantum error

correction you need.

Spins in silicon have extraordinary

coherence properties for solid-state

quantum systems while being

compatible with

CMOS.C. Tahan et al.

phonon



A quantum well quantum dot

Si substrate

Step graded

Silicon-Germanium

Si0.75Ge0.25

Si0.75Ge0.25

Strained SiQuantum

Well

(6-12 nm)

Step graded SiGe

Si cap layer

Phosphorous donor atoms130 meV

z

- -- - - -- - - -- - - -

- - -

- - -

-

- - -

-

Metal

gates

-V (volts)

single electron

wave function

Goal: a single electron tunably confined vertically and horizontally in a semiconductor nanostructure

20-100 nm



2, we need a way to make a CNOT 2-qubit gate

J ≅≅≅≅ 0

Uncoupled

J > 0

Swap

H2 quantum dots → Heff = J s1·s2

SWAP: Int[J(t) dt] = πħ

SWAP doesn’t entangle but Sqrt[SWAP] does.

=> CNOT



Simulation: Coupled Qubits in Silicon

(Friesen, Rugheimer, Savage, et al., ’03)

on

off

screened

potential

probability

density

J =

20 µeV

J � 0S =↑↓ − ↓↑

2

T =

↑↑↑↓ + ↓↑

2↓↓

J = ES − ET

Simulation


Available at http://www.tahan.com/charlie/43Petta et al., Science 309, 2180 (2005).

(0,2)S

ε

2t

Energ

y

(0,1)

(1,1) (1,2)

(0,2)

(1,1)S

(1,1)S (0,2)S

(1,1)T0

Singlet preparationSinglet separationEvolutionProjectionReset

(0,2)(1,1)

S

ST

(1,1) (0,2)

S

ST

(1,1) (0,2)

S

ST S

(0,2)(1,1)

ST

(1,1) (0,2)

S

ST

Dephasing causes a failure to return to (0,2)

GaAs DQD Spin Qubits

Harvard – Science 309, 2180 (2005)

Petta et al., Science 309, 2180 (2005).

Exch

an

ge

Re

gio

n

Slide courtesy M. Biercuk



Powerpoint is great isn’t it?

• Quantum dot quantum computerThe glory of being a theorist.

Charles Tahan, Cambridge University, http://tahan.com/charlie/

The N

ew

Idea

Example 2: Solid Light

1. Array of quantum optical cavities

2. Each cavity has 2 Level System + photon(s)

3. Coupled by photon hopping/overlap

4. Photon interaction mediated by 2LS nonlinearity

= atom + photon(s) composite particle or “dressed”-state or polariton

Engineer a system where photons will interact strongly and exhibitquantum many-body

dynamics in an interesting and perhaps useful way.

With Andy Greentree et al., University of Melbourne (Nature Physics ‘06)


Backgro

und

Photons…

1. Don’t interact with each other much

2. Great for communication, not for computation

3. Aren’t conserved (created or destroyed at will)

4. Can be made coherent easily (lasers) - unlike

matter

5. Can’t exhibit the behavior that “strongly

interacting” particles like electrons do

How can we make photons exhibit

quantum many body behavior?



Microwave stripline cavity + Cooper Pair Box (Yale)

Diamond PBG cavity + color center complex (Melbourne)

Backgro

und

Cavity-QED: From atomic to solid-state




Microwave stripline cavity + Cooper Pair Box (Yale)

Diamond PBG cavity + color center complex (Melbourne)

Backgro

und

Cavity-QED: From atomic to solid-state


On-site repulsion, U:

photon blockade!

Matter-induced photon-photon nonlinearity


An Im

ple

menta

tion

Step 1

waveguide in the

growth direction

Diamond single crystal slab

λ /2

Photonic superlattice in a NV/Diamond photonic bandgap architecture

polished surfaces


An Im

ple

menta

tion

Step 2

Drill holes selectively to create superlattice of defect-cavities (aka quantum optical cavities)



An Im

ple

menta

tion

Step 2

Drill holes selectively to create superlattice of defect-cavities (aka quantum cavities)

Quantum optical

cavity



An Im

ple

menta

tion

Step 3 Create NV- complex in each cavity


An Im

ple

menta

tion

Step 4 Add photons (say with a coherent laser pulse)

= Extent of dressed-atom

photon trapped in each cavity.

Hopping is allowed to nearest neighbor

cavities via evanescent coupling.


Physic

al M

odel

Hamiltonian

photon hopping conserved# of excitations

Jaynes-

Cummingstwo-level system photons atom-light coupling


Theore

tical A

naly

sis

QPT0 detuning

No disorderT = 0

photon hopping

rela

tive c

hem

ical

po

ten

tial

su

perflu

id o

rder p

ara

mete

r

0 photons

1 photon

2

BH model


Conclu

sio

ns a

nd Q

uestions

Impact• “Engineered” quantum many-body interaction

of photons (dressed)

• Predict gapped Mott insulator phase (exactly n photons per site) to superfluid transition

• Each site directly accessible (cavity volume comparable to wavelength of light) - optical fiber probe?

• Possible uses: quantum simulator (very tunable); loading of many single photon sources; ?

• IMPLEMENTATIONS: InAs QDs in PBGs, microwave strip-line cQED arrays, Rb atom arrays in high-Q superconducting cavities; NV/diamond, microcavities



Generating entangled photons

1. An ultraviolet laser sends a single photon through Beta Barium Borate.2. As the photon travels through the crystal, there is a chance it will split.3. If it splits, the photon will exit from the Beta Barium Borate as two photons.

4. The resulting photon pair are entangled.



“Entangled-Pair Shotgun”





Neil Na and Yoshi

Yamamoto, Stanford



Example 3: Phase estimation

• Precision measurement of length, displacement, speed, optical properties, etc.

• Primitive or subroutine for quantum algorithms (like Shor’s)

• Using phase for communication, etc.

Source:

Physics Team PROPRIETARY – FOR INTERNAL BOOZ ALLEN HAMILTON USE

Optical source

MirrorBeam splitter

Mirror

Sample

Processor

Detector

φ

Mach-Zender

interferometer

Quantum tricks can reduce the number of photons needed by

SQRT(N)



Almost done










The US then, the world now

The rest of the world now



Annual "Quantum" Publications

0 6 5 10

5 23

22

21 28 38 45 51 81 95

67 1

13

13

3

1 2 2 4 4 22

20 29

11

6

10

9 20

0

22

6

367 437

394

63

0

51

9

0

200

400

600

800

1990 1992 1994 1996 1998 2000 2002 2004 2006 Year

Nu

mb

er

of

Pu

blicati

on

s

Communications

Computation

Quantum Information Activity Worldwide

Published References by RegionQuantum Communications

Results based on ISI Web of Science

search for publications containing the

phrases “quantum computat*,”

“quantum bit,” “qubit,” or “quantum

informat*,” from 1990-2006.

N. America199

Europe390

Asia189

Published References by RegionQuantum Computation

Results based on ISI Web of Science

search for publications containing the

phrases “quantum cryptography,”

“quantum key,” “QKD,” or “quantum

communicat*,” from 1990-2006.

N. America1051

Europe

1256Asia555



6 months later: the sound of crickets

chirping on the internet



The end

• More information:

– http://www.tahan.com/charlie/

It is not only the speed of technological change that creates a “revolution,” it is its scope as well. Above all, today, as seven thousand years ago, technological developments from a great many areas are growing together to create a new human environment. (Drucker, 1965)



Backups



Quantum Algorithms /Computer Science,Math

A universal set of gates can compute an arbitraryfunction (e.g. NAND for classical computation)

Single qubit gates and CNOT are a universal set of gates for quantum computation.

=

0100

1000

0010

0001

CNOTU

CN

OTψ

ψ

Universal Quantum Computation

qubit 1

qubit 2

1 qubit rotation



=

0100

1000

0010

0001

CNOTU

CN

OT|0⟩⟩⟩⟩

|0⟩⟩⟩⟩|0⟩⟩⟩⟩|0⟩⟩⟩⟩ >>

|0⟩⟩⟩⟩>>|0⟩⟩⟩⟩|0⟩⟩⟩⟩

|0⟩⟩⟩⟩C

NO

T|0⟩⟩⟩⟩

|1⟩⟩⟩⟩|0⟩⟩⟩⟩|1⟩⟩⟩⟩ >>

|0⟩⟩⟩⟩>>|0⟩⟩⟩⟩|1⟩⟩⟩⟩

|1⟩⟩⟩⟩

CN

OT|1⟩⟩⟩⟩

|0⟩⟩⟩⟩|1⟩⟩⟩⟩|0⟩⟩⟩⟩ >>

|1⟩⟩⟩⟩>>|1⟩⟩⟩⟩|1⟩⟩⟩⟩

|1⟩⟩⟩⟩

CN

OT|1⟩⟩⟩⟩

|1⟩⟩⟩⟩|1⟩⟩⟩⟩|1⟩⟩⟩⟩ >>

|1⟩⟩⟩⟩>>|1⟩⟩⟩⟩|0⟩⟩⟩⟩

|0⟩⟩⟩⟩

CNOT



=

0100

1000

0010

0001

CNOTU

CN

OT

|0⟩⟩⟩⟩

|0⟩⟩⟩⟩

H |0⟩⟩⟩⟩+|1⟩⟩⟩⟩ |0⟩⟩⟩⟩+|1⟩⟩⟩⟩

|0⟩⟩⟩⟩+|1⟩⟩⟩⟩?>> (|0⟩⟩⟩⟩+|1⟩⟩⟩⟩)(|0⟩⟩⟩⟩+|1⟩⟩⟩⟩)NO!!!!!!!!!!!!

CNOT

(|0⟩⟩⟩⟩+|1⟩⟩⟩⟩)|0⟩⟩⟩⟩ = |00⟩⟩⟩⟩ + |10⟩⟩⟩⟩

CNOT[ |00⟩⟩⟩⟩ + |10⟩⟩⟩⟩ ] = |00⟩⟩⟩⟩ + |11⟩⟩⟩⟩

The state cannot be written on two separate lines.

=> entangled state



• Single qubit rotations on the Bloch sphere

=

01

10X

−=

0

0

i

iY

−=

10

01Z

−=

11

11H

=

)4/exp(0

01

πiT

X

Y

Z

H

T

ψψ h/iHteU

−=

2/XieU

θ−=10 =X

2

100

+=H

One qubit rotations



Quantum Power

• Superposition (and large Hilbert space)

• Entanglement

• Interference (waves)

But we need to ask the right questions.

Review



Quantum Parallelism

x

y y ⊕ f (x)

x

f(x) is a binary function: f ( 0,1{ }) = 0,1{ }

0 + 1

2

0

ψ =0, f (0) + 1, f (1)

2

ψ



Deutsch Algorithm

x

y y ⊕ f (x)

x

Ask a global question: Is the function f(x) constant or not?

0 + 1

2

0 − 1

2

H

ψ = ± f (0) ⊕ f (1)0 − 1

2

ψ

Qubit 1 encodes the answer to the global question.



Quantum Teleportation

ψ

Want to send the state psi from alice to bob.

00 + 11

2

CN

OT

Bob

AliceH

M1= 0 or 1

M2= 0 or 1

XM2 ZM1 ψThe qubit state is transferred from Alice to

Bob utilizing the entanglement of the Bell

state as a resource. It is not copied.



No cloning theorem

No cloning theorem: it is NOT possible to make a copy of an unknown quantum state

Classical copying circuit:

x ⊕ y

x

0

xx x

xy⇒ xx

x ⊕ y

x

0

xψ = a 0 + b1

y

⇒ a 00 + b11

Quantum version

ψ ψ = a2 00 + ab 01 + ab10 + b2 11But,



QEC - Active

No cloning theorem: it is NOT possible to make a copy of an unknown quantum state

The Shor code: 9 qubits

ψ

0

H

0

CN

OT

CN

OT

0

H

0

CN

OT

CN

OT

0

H

0

CN

OT

CN

OT

0

0

CN

OT

CN

OT

−−−=→

+++=→

L

L

11

00

11111

00000

=→

=→

L

L

phase flip code

bit flip code

Threshold theorem



Digital Quantum Error Correction

(t+1)k

δδδδ(k)=pth(p/pth)

Unclassified

QECConcatenation

This rate can, in principle,

be made small enough to

perform large calculations

Resources grow exponentially



Shor’s Algorithm Overview

• Quantum-Fourier-Transform-based algorithm

• Leverages classical protocols relating factoring to order finding

• Requires modular arithmetic to produce a function whose QFT provides the order we’re seeking

• All useful information derived from the period of a function: collapse of Fourier-transformed state on measurement does not impact utility

• Modular arithmetic permits classical computing circuits to be adapted to quantum computation

Choose

random

x<N

Create

superposition

of all possible

exponents xj mod N

Quantum

Fourier

Transform

& Measure

Classical

processing to find

order r from

measurement

result. May require

multiple runs

Classical

postprocessing

to find factors

from r.

Shor’s Algorithm Logical Organization

Choice of Adder



Factoring Number Theory

• We wish to factor N=pq, a composite of two primes

• The order r is defined by the following: (given a randomly selected xrelatively prime to N). This indicates that r is an exponent which makes this function periodic.

)(mod1 Nxr ≡

• If r is even then we can write the equation as follows:

)(mod0)1)(1(

)(mod01)(

)(mod01

2/2/

22/

Nxx

Nx

Nx

rr

r

r

≡+−

≡−

≡−

• Therefore this product must be an integer multiple of N

• Assuming neither term is itself a multiple of N we find the factors using (if this fails, we select a new x and try again)

),1gcd( 2/Nx

r ±

To find the factors of N we need to find the order, r, of xj(mod N)

Shor’s algorithm exploits quantum parallelism to find r efficiently

Charles Tahan, Cambridge University, http://tahan.com/charlie/Conclu

sio

ns a

nd Q

uestions

More Information

http://tahan.com/charlie/

Andrew Greentree, Charles Tahan, Jared Cole, Lloyd Hollenberg,

“Quantum phase transitions of light,” Nature Physics 2, 856 - 861

(December, 2006)

‘News and Views’ - Nature Physics, December 2006

“Engaging photons in light conversation,” New Scientist, Jan. 11th, 2007

http://arxiv.org/abs/cond-mat/0609050

Using condensed matter physics to control photons

QPTωOverview

Motivation

Circumstances

The New Idea

Background

An Implementation

Physical Model

Theoretical Analysis

Numbers

Conclusions and Questions

Using condensed matter physics to control photons


Charles Tahan, Cambridge University, http://tahan.com/charlie/An Im

ple

menta

tion

Diamond

• Hardest material

• Highest thermal conductivity

• Extremely chemically inert

• Widest transparency window

• Well defined (spin zero) lattice

• Large electrical breakdown voltage

• Huge number of defects and dopants

• (near) Atomic placement of defects

• Great quantum properties (coherence)

• Drives girls crazy

Charles Tahan, Cambridge University, http://tahan.com/charlie/An Im

ple

menta

tion

Diamond 2• Photonic band-gap (PBG) structures

• Waveguides

• Many impurities - color centers

• Solid-state cavity QED

• Q-switches to outcouple photons

So if you want to learn

quantum optics…


Available at http://www.tahan.com/charlie/83B

ackgro

und


NV (nitrogen-vacancy) color center in diamond

3A

3E1A

• Optical transition at 638 nm

• Stark tunable

• Precision Implantation

electric-dipole transition

1. Room temperature single photon source? Quantum Communication

2. Spin-based Quantum Computing?



Parameters, Rb vs NV-

~10 µm3>103 µm3Cavity volume

1010 Hz ?120 MHzSingle photon

coupling

105-10 ???106Q

1×10-29 Cm1×10-29 CmDipole Moment

24 MHz20 MHzHomogeneous

Linewidth

638 nm780 nmWavelength

[NV]-Rb – D2 line

from A. Greentree



Phase estimation

• Precision measurement of length, displacement, speed, optical properties, etc.

• Primitive or subroutine for quantum algorithms (like Shor’s)

• Using phase for communication, etc.

Source:


Optical source

MirrorBeam splitter

Mirror

Sample

Processor

Detector

φ

Mach-Zender

interferometer



Interferometry (qubit version, Ramsey)

•

• Beam splitter:

• Sample:

• Beam splitter:

• So

• If we evaluate a parameter Φ from a quantity p(Φ), error propagation theory tells us that ther error is

• If we repeat N times, standard deviations gives

Source: Giovennetti et al 2004


Optical

source

MirrorBeam splitte

r

Mirror

Sample

Processor

Detector

φ

Mach-Zender

interferometer

C

D

( ) ( )2/cos|p) Prob( 22

φφ ==≡= outinoutin

1=in

( ) 2/10 +

2

1

( ) 2/10 φie+

( ) ( )( )

=

==

=++−

...

0 if 0

if 1

2/1010 φ

πφφ

in

ei

( ) ( ) ( ) ( ) ( )φφφφ 2222 :error lstatistica with estimated pppoutininoutp −=−=∆

( ) ( )1/ =

∂∆=∆

φφ

φφp

p

N/1=∆φ

3

4



“Standard quantum limit”

• “Sweet spot” where you minimize noise and maximize sensitivity (number of photons versus mirrors shaking)

– Re: Michelson: Balance of two sources of error: the error in determining z

due to fluctuations in the number of output photons and the perturbation of z

during a measurement produced by fluctuating radiation pressure forces on

the end mirrors. As the input laser power increases, the photon-counting

error decreases, while the radiation pressure increases.

• NOT a fundamental limit

• Originates from a non-optimal choice of measurement strategy

• N single photon devices OR device with N photons

• Shot noise: environment-induced noise from vacuum fluctuations (entering the interferometer from the unused input port) that affects the measurement of the electromagnetic field amplitude, and the dynamically induced noise in the position measurement of a free mass

Source:




Heisenberg limit

• Heisenberg uncertainty relation of two dual observables:

• Suppose (N+1)-level system, angular momentum

representation

• Want minimum uncertainty in Q (so maximize uncertainty

in Jz)

• Choose equal distribution of Jz eigenstates:

• The variance is then:

• Then

Source:


( )NQ

NQJQ z

/1ˆ

2/1ˆˆˆ 2

∝∆⇒

≥∆=∆∆

( ) ( ) miNN

Nm

m∑−=

−+=2/

2/

2/1exp1 φψ

mmmJ z =ˆ

( ) 22

222

243

1ˆˆˆ NNN

JJJ zzz ∝

+=−=∆ ψψψψ

scaling!in t improvemen N

2/1ˆˆ ≥∆∆ zJQ



History: ideas to get to Heisenberg

limit• Squeezed states (Caves, 1980)

– Normally one quadrature is thrown away -> Squeeze vacuum input mode

– N-3/4 scaling (beats standard quantum limit)

– Very little experimental success in last 25 years

• Correlated input states (Yurke, 1986, Douling, Milbunrn, etc.)

– Use entangled light

– Get to 1/N limit in theory

– Maximally entangled states of many photons are really hard to make

– Requires high n detectors (not known how do measurement)

• Real-time quantum feedback loop (Wiseman, 1995, 97, 00, Mabuchi et al)

– Use feedback loop instead of entanglement

– Use data from previous photon statistics to estimate Φ and tune phase to second arm of interferometer

– Must be done in real time (processing must occur in between photon events)

Source:




Entanglement

• Instead of using N times the state |in> use the N00N state

• N00N state:

• The tensor product nature of quantum mechanics helps us, as the exp(iΦ) phase factors gained by the |1>s combine so that

• Improved phase sensitivity results from a decrease in the phase period from 2π to 2π/N

•

Source: Giovannetti / Dowling


[ ] [ ]ABABNN

NNin ,00,2

11100

2

100

+=+= KK

H

CN

OT

CN

OT

CN

OT

…

[ ]11002

1KK

φiNeout +=

( ) ( )2/cos is y that probabilit The 2 φφ Nqoutin ==

( ) ( ) ( )φφφ 22error with qqq −=∆ ( ) ( )/N

qq 1/ meanswhich =

∂∆=∆

φφ

φφ



Entanglement

• Interferometry: a N00N state of 10 photons each of wavelength λ acts like 1 photon of wavelength λ /10

– So resolution is much better than diffraction limit (λ/4)

• Same thing for clocks!

– The more “ticks” of your clock, the better the precision

– 10 atoms with frequency ω act like atom with energy 10 ω

– Demonstrated by Wineland group

• Lithography

• Imaging

• But maximally entangled state beyond 2 photons are hard to produce

– (You basically need a photonic quantum computer to do it – with error correction!)

Source: Many


Charles Tahan, Cambridge University, http://tahan.com/charlie/Theore

tical A

naly

sis

Mott plateaux

ρ =∂Eg ψ =ψmin( )

∂µ

Mott lobes indicate regions of constant density and incompressibility

excit

ati

on

den

sit

y

Charles Tahan, Cambridge University, http://tahan.com/charlie/Theore

tical A

naly

sis

Mean-field Approach

: # nearest

neighbors

• Success in cold atom optical lattices and polariton systems

(verified with QMC and other) - obvious first step

Charles Tahan, Cambridge University, http://tahan.com/charlie/Num

bers

Will it work NV-Diamond numbers



Quantum information overview

• Basic understanding of quantum physics developed in the 1920s.

• The second phase of quantum-designed technologies take advantage of the less-understood and largely swept-under-the-rug properties of quantum mechanics.

• Spookytechnology and Society

– work in Nanotechnology and Society education and my physics research in quantum computing and condensed matter theory

– the history of nanotechnology as a guide

– societal considerations taking place in the Nano+Society community

– proposal for new terminology (which may be controversial for some)

– initiate a framework for considering the educational and societal issues in the physics community, before the science fiction or popular culture can distort the reality, as happened with nanotech.

– bridge the gap with the science and technology studies community, who will be a partner with physics researchers and educators as quantum information and related technologies go mainstream.



1, We need a good qubit

Spin-1/2

B

Spins make good qubits!

• Natural two-level quantum system

• Good isolation from charge fluctuations

• Historical record of long lifetimes in semiconductors

• Well-developed techniques for manipulation (NMR, ESR)

• Well-known interaction Hamiltonians- Spin exchange (FAST), Magnetic dipole-dipole

• Compatibility with semiconductor infrastructure (scalability)



Exchange-based QC

C. Tahan

8/17/2005

D. Loss & D. DiVincenzo

B. E. KaneGaAs/AlGaAs

Si/SiGe

Carbon Nanotubes



Towards quantum

E >> kT ⇒ quantum

smaller

colderAt room temperature, kT=26 meV



spookytechnology and society - stanford university · nanotechnology is the creation of functional...

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