Oct 25, 20051 Program Perspectives on Quantum Information Michael Foster National Science Foundation.

Oct 25, 2005

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Program Perspectives on Quantum Information

Michael Foster

National Science Foundation

Oct 25, 2005

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Outline

• Computing & Communication Foundations

• QIS Bumper Stickers

• Quantum Computing

• Quantum Key Distribution

• Support agencies

• Where next?

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Why Foundations?

-=

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Foundations Everywhere

Infrastructure

Systems

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Quantum InformationBumper Stickers

• Quantum computation– State superposition provides parallelism

• Quantum communication– No cloning theorem provides unforgability

• Quantum metrology– Entanglement provides consistent measurement

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Quantum Computation

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QIP and Moore’s Law

Year

1850 1950 20001900 2050

10-6

103

1

10-3

106

109

Babbage Engine

CMOS ICs

TX-2

ENIAC

Differential Analyzer

GeneralArchitecture

Lattice-GasArchitecture

Quantum Dots

Liquid NMR

Conve

ntio

nal C

ompu

ter R

oadm

ap

QC

Roa

dmap

MIPS

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Power of Qubits

•Qubit = state of a quantum two-level system

1,1022 Continuum of states!

1 classical bit has two states: 0 and 11 qubit has “infinitely” many states!

•Physical realizations of qubits:•photon polarization•electron spin•nuclear spin•pair of electron states in a trapped ion/atom•magnetic flux state in a Josephson junction ring•Cooper pair number states, etc.

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Power of Qubits

A classical 3-bit state: 001A quantum 3-qubit state:

111110101011100010001000

N qubits is worth 2n classical bits!•Entanglement

•Multiple qubits

101011100100

1001

1100

Not entangled

Entangled!

PhotonsOptical

Parametric Amplifier

OpticalParametric Amplifier

EPR photon pairEPR photon pair

or

NEVER

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Power of Quantum Computation

•Quantum Parallelism

An exponential amount of computation has been achieved in the time it takes to compute the function on a single input!

2n values of F(x) all in one go!!

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NP BQP?

Provably Q-hard algorithms

PSPACE

BQP

P

NP

Factorization (Shor)

Unsorted Search(Grover)

GraphIsomorphism?

Protein Folding?

Ajtai–Dwork Coding?

Quantum Complexity

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Permutation Order-Finding (Chuang et al, ‘00)•Permutation is an operation that rearranges a set of objects

•Order r of a permutation applied to element y of a set is the minimum number of times must be applied to put y back in its original position

•Problem has wide range of applications (Cryptography)

QIP: An Example Algorithm

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Classical versus Quantum

Classical approach:•Series of trials to find the x-th permutation x(y).

•Find equality. When a(y)= b(y) then ord() | a-b

•Number of trials needed increases exponentially with the number of bits representing y

Quantum approach:•Order is the period of a functionfy(x) = x(y)

•Quantum Fourier Transform allows us to find periods of all x(y) with one transform

•Exponential speedup-- Minimum number of steps proportional to bits in y

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Classical Order-Finding

2

3

rYY

3

7

AA

QQ

ZZ

MM

AA

FF

2

26

15

Check Equality

Classical approach:

What a permutation really looks like:

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Quantum Order-Finding

YY

3

7

AA

QQ

ZZ

MM

AA

FF

2

26

15

Quantum approach:

Equality

Large Fourier Components

Quantum Fourier

Transform

Checks Equality in

Parallel

Likely result

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Quantum Fourier Transform (QFT)

• Variant of the Discrete Fourier Transform (DFT) that can be implemented on a quantum computer

• At the heart of Factoring and Order-Finding problems• QFT transforms state amplitudes to state amplitudes

– NOT qubits to qubits

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QFT in Order Finding

x

y

H HR

Superpose QFTMeasure

x(y)

•States are measured according to their probability

•Many states at P produce the same x(y)

•QFT produces their frequency

•Probably answer reflects large number of states at P

PAnswer

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Status of Computing

• Proof of concept factoring (2001)Chuang et al. 4-bit Shor algorithm implementation (2001)

•Ongoing ion-trap implementation effort

•Some optical lattice efforts

•Solid-state spins moving slowly

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Ion Trap Investigations

• Done (per ARDA Roadmap April 2, 2004)– 2-qubit operations demonstrated– Long decoherence times in progress– 3-10 qubit operations started

• Proposed (individual researchers)– 10-20 qubit registers– Architectures with 1000 circulating qubits

• Possibility– 20 logical qubits (2-level error correct 1000 qubits)– 10 bit factoring

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Optical Lattices

• Done (individual researchers)– 110 site lattice loaded from BEC with 200

atoms/site

• Proposed (individual researchers)– 8000 sites with CO2 lasers proposed by

Berkeley QuIST project• Filling factor 1/2

– Permits 80 logical qubits– Permits 40 bit factoring

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Architectural Roadblocks

• Classical control– Large feature sizes for control lines mean large computers

• Wiring and corners– Moving qubits leads to decoherence

• Error correction– More check bits than data bits

• Cumulative effect– May need 100,000 times longer decoherence times than

required by operations alone (Balensiefer et. al, ISCA32, 2005, pp186-196).

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Quantum Security

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Quantum Key Distribution

• Use unforgability to detect eavesdropping

• Shared generation of secure key

• Extensive classical processing

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Status of Key Distribution

QKDEndpoint

Encrypted Trafficvia Internet

QKDEndpoint

QKD Switch QKD Switch

QKD Switch

QKD Switch

QKD Repeater

PrivateEnclave

PrivateEnclave

Ultra-Long-Distance Fiber

End-to-End Key Distribution

BBN-AFRL-QuIST Network Rollout June 1, 2004

NEC 2-week demonstration May 31, 2005 (AFRL-QuIST inside?)

13kb/sec sifted key over 16km commercial access optical network

ID Quantique Turnkey System

Available throughout Switzerland June 05

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Support Agencies

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DARPA Mission

Focused strategic thrusts

Specific programs

Emphasize transition

Source: Bridging the Gap February 2005

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DARPA Organization

Source: Bridging the Gap February 2005

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QIP in DARPA Organization

Source: Bridging the Gap February 2005

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NSF Mission

National Science Foundation Act of 1950 (Public Law 810507):

• To promote the progress of science; • to advance the national health, prosperity,

and welfare; • to secure the national defense; • and for other purposes.

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NSF Organization

D ire c to ra te fo r B io lo g ica lS c ie n ces

D ire c to ra te fo r M a th e m a tica l& P h ysica l S cie n ces

D ire cto ra te fo r C o m pu te r &In fo rm atio n S cie n ce an d E n g in e ering

D ire c to ra te fo r S o cia l, B eh v io ra l& E con o m ic S c ie n ces

D ire cto ra te fo r E d u ca tion& H um a n R e sou rces

D ire c to ra te fo r G e o sc ie n ces

D ire cto ra te fo r E n g ine e ring O ffice o f P o la r P ro gra m s

O ffice o f In te gra tive A c tiv it ies

O ffice o f the D ire c to r

N a tion a l S cie n ceB o a rd

Administrative Offices

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QIP in NSF Organization

D ire c to ra te fo r B io lo g ica lS c ie n ces

D ire c to ra te fo r M a th e m a tica l& P h ysica l S cie n ces

D ire cto ra te fo r C o m pu te r &In fo rm atio n S cie n ce an d E n g in e ering

D ire c to ra te fo r S o cia l, B eh v io ra l& E con o m ic S c ie n ces

D ire cto ra te fo r E d u ca tion& H um a n R e sou rces

D ire c to ra te fo r G e o sc ie n ces

D ire cto ra te fo r E n g ine e ring O ffice o f P o la r P ro gra m s

O ffice o f In te gra tive A c tiv it ies

O ffice o f the D ire c to r

N a tion a l S cie n ceB o a rd

Administrative Offices

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CISE Mission

• to enable the United States to remain competitive in computing, communications, and information science and engineering;

• to promote understanding of the principles and uses of advanced computing, communications, and information systems in service to society; and

• to contribute to universal, transparent, and affordable participation in an information-based society.

CISE has three goals:

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Desired Project Characteristics

• DARPA – Fast Results– Military need

– Technical challenges and plan for meeting them

– Transition plan

• NSF – Sustained Effort– Asks fundamental questions

– Maintains U.S. competitiveness

– Societal need

– Broad participation

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DARPA Program Highlights

QKDEndpoint

Encrypted Trafficvia Internet

QKDEndpoint

QKD Switch QKD Switch

QKD Switch

QKD Switch

QKD Repeater

PrivateEnclave

PrivateEnclave

Ultra-Long-Distance Fiber

End-to-End Key Distribution

QuIST Network Rollout June 1, 2004

Chuang et al. 4-bit Shor algorithm implementation (2001)

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NSF Program HighlightsInstitute for Quantum

Information at Caltech

CAREER Award: Yaoyun Shi at U. Michigan

Quantum Complexity and Polynomial Approximations of Boolean Functions

– Quantum and classical tradeoffs

– Classical simulation of quantum communication.

– Phase transition in biological signaling systems

– Education plan: theory of computation courses

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Where Next for Communication?

• DARPA– Long range demonstrations between metronets– GtoA and GtoS demonstrations– ConOps for QKD

• NSF– New protocols– Security bounds

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Where Next for Computation?

• New algorithms– Exponential speedups, please!– (Hashing outdoes unstructured search)

• New applications of existing algorithms– Pell’s equation– Random walk

• Scalable architectures– Controllable– Fault tolerant

• Medium-scale implementations– 10’s of qubits– Probably beyond NSF resources

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The Near Future

• NSF budget is down 3% in 2005, looks flat

• DoD will need transitions beyond crypto

• New algorithms and protocols are needed for the next push– Scalable architectures too

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The Want Ads

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Program Directors Sought

• Numeric, Symbolic, Geometric computing

• Emerging Models and Technologies

• Interdisciplinary capability– Across cluster, division, NSF, and globally

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Contact

• Vacancy announcements appear on www.nsf.gov• Meanwhile contact

Michael Foster

Division Director

Computing & Communication Foundations

National Science Foundation

4201 Wilson Boulevard

Arlington, VA 22230

703-292-8910

[email protected]