Basic Principles of Quantum computing I

Soonchil LeeDept. of physics, KAIST

• 1 MIPS 컴퓨터로 1016 개의 자료 중 하나를 찾을 때– 고전컴퓨터 : 300 년– 양자컴퓨터 : 1 분

• 현대 암호는 모두 NSA 에서 개발양자전산 개발을 늦추면 암호종속모든 정보의 일방적 유출

양자전산의 중요성

Quantum computingQuantum computing

/0 iHt

i Ht

e

OUTPUT U INPUT

Classical computingClassical computing

INPUT OUTPUT

GATE

Ex) NOT operation

/0

U

iHte

1Assign 0

0

0 1

1

0 1We need

1 0U

For H H ,

exp( H / )=exp( )x

x x

H I

U i I t i tI

((((((((((((((((((((((((((((

Set t 0 1

exp( ) exp( )1 02x x xU i I i i i

H

0

10 1i

1 0i

고전전산 양자전산

비트상태 전압 0V & 5V 상태

양자고유상태 - 중첩가능중첩가능Ex)spin up & down Photon olarization

연산자 반도체게이트 Unitary operationUnitary operation진화연산자Optical deviceOptical device

알고리듬 수행

게이트의 공간적 배열을 비트가 통과

고정된 비트에 연산이 시간적으로 수행됨

Classical computingClassical computing

INPUT OUTPUT

GATE Ex) ADDER

Quantum computingQuantum computing

INPUT OUTPUT

GATE Ex)

U1 U2 U3

t

U1

U2

U3

Execution of quantum algorithmExecution of quantum algorithm

(1) Algorithm development = a unitary operator U

(2) Decomposition of U : U=U1U2U3… (programming)

where and Hi is a part of

(3) Real pulse sequence design (compile)

exp( / )i iU iH t

,

(rf pulse) (J-coupling)

i i ij iz jzi i j

H I J I I

Any unitary operator can be expressed as a sequenceof single qubit operators and controlled-NOT operators.

0

0

dL

dt

M H

L H

0H

Single qubit operation

H

M

|1>

|0>

* Single qubit operation

( ) exp( / )

exp( ( ) / )

exp( )

exp( )

i i

i i

i i

i

R iH t

i I t

i tI

i I

i i iH I 0 1

1( 0 1 )

2

1( 0 1 )

2

1( 0 1 )

2i

1( 0 1 )

2i

Single qubit operationis done by an rf pulse.

* Controlled-NOT operation

Controlled-NOT gate

input output

C T C T

0 0 0 0

0 1 0 1

1 0 1 1

1 1 1 0

( 0 1 ) 0 : disentangled state

0 0 1 1 : entangled state

U

1 2 2 12 2( ) ( ) ( ) ( ) ( )2 2 2 2 2

C NOT

z x y y

U

R R R U R

where

and

( ) exp( )i iR i I

( ) exp( ( ) / )

exp( ( / ) )

exp( )

ij ij iz jz

ij iz jz

iz jz

U i J I I t

i J t I I

i I I

Controlled-NOT is doneby just waiting.

Controlled-NOT

input output

C T C T

0 0 0 0

0 1 0 1

1 0 1 1

1 1 1 0

( 0 1 ) 0 : disentangled state

0 0 1 1 : entangled state

U

|10>

|11>

|01>

|00>

UCT

CT

5 4 3 2 1 3

f(x)=0Classical computing

|1>+|2>+|3>+….

f(x)=0

|3>

Quantum computing

Quantum parallel processing

• Classical parallel processing cannot imitate because

1. N qubit represents 2N states. 2. entanglement

|1>+|2> = |0>A|1>B+|1>A|0>B

• Shor’s factorization algorithm– QC : (logN)2+x steps (x<<1)– classical computer : exp{N1/3(logN)2/3}– 공개열쇠암호체계 격파

• Grover’s search algorithm– for N data search, QC : N1/2 try classical computer : N/2 try ex) if N=256 & 1 MIPS, 1000 year vs. 4 min.– 비밀열쇠암호체계 격파

핵자기공명 (NMR: Nuclear Magnetic Resonance)

- 대표적인 핵스핀 조작기법

1) J. Kim, J.-S. Lee, and S. Lee, Phys. Rev. A 61, 032312 (2000).2) J. Kim, J.-S. Lee, S. Lee, and C. Cheong, submitted to Phys. Rev. A

Requirements for a Quantum ComputerRequirements for a Quantum Computer

(1) qubit : two quantum states with good quantum #

(2) Set : by measurement or thermal equilibrium ex)

(3) Read(4) Single qubit operation (addressible):

physical addressing or resonance tech.

(5) Interaction (controllable) :well defined and on-off

-------------------------------------------------------------(6) Coherence : isolation from environment (and other qubits)

(7) Scalability

( exp( / ) exp( ))H S U iHt tS

( )i jij

H JS S

(1) qubit - two states with good quantum #

•energy : el. floating in LHe•charge : quantum dot•spin : quantum dot, molecular magnet, ion trap,

NMR, Si-based QC•photon : optical QC, cavity QED•cooper pair : superconductor•fluxoid : superconductor

Requirements for a Quantum ComputerRequirements for a Quantum Computer

(1) qubit : SPIN(2) Set : by measurement or thermal equilibrium

ex)

(3) Read(4) Single qubit operation (addressible):

physical addressing or resonance tech.

(5) Interaction (controllable) :well defined and on-off

(6) Coherence : isolation from environment (and other qubits)

( exp( / ) exp( ))H S U iHt tS

( )i jij

H JS S

(6) Long coherence : Isolate qubits

•in vacuum : ion trap, el. floating in LHe•by flying : methods using photon,

el’s trapped by SAW or magnetic field•in molecule : NMR•in quantum well : quantum dot, superconductor•inside solid : Si-based QC

Requirements for a Quantum ComputerRequirements for a Quantum Computer

(1) qubit : SPIN(2) Set : by measurement or thermal equilibrium

ex)

(3) Read(4) Single qubit operation (addressible):

(5) Interaction (controllable) :well defined and on-off

(6) Coherence : solid state device

( )i jij

H JS S

Magnetic Resonance Force Microscopy (MRFM)

- Scanning Probe 와 공명의 결합

- 단일스핀 감지

Requirements for a Quantum ComputerRequirements for a Quantum Computer

(1) qubit : SPIN(2) Set (3) Read : Single spin detection(4) Single qubit operation (addressible):

(5) Interaction control

(6) Coherence : solid state device

( )i jij

H JS S

Ion trapIon trap

Qubit - ion spin stateSingle spin operation - laserInertaction - vibration(CM motion)

Environment

measurementfield

Basic Principles of Quantum Basic Principles of Quantum computing IIcomputing II

Soonchil LeeDept. of physics, KAIST

10 years ago…

• 1st demonstration of quantum computing by NMR

For 5 years after then…• We were excited by new challenge.• Had a hard time to understand new

concepts.• Lots of NMR QC papers were published.• Realized keys of a practical QC.• Pedestrians show interests.• Found that NMR is NOT a future QC.• NMR QC experiment is needed no more.

Things change. Now…

• Developing a Practical Quantum Computer is the key issue.

TheoryExperiment

Electron beamElectron beamel. floating on liquid Heel. trapped by SAWel. trapped by magnetic field

Atomic and MolecularAtomic and MolecularIon trapCavity QEDNMRMolecular magnetN@C60(fullerine)BEC

Solid StateSolid State Quantum dotSuperconductorSi-based QC

Optical Optical PhotonPhotonic crystal

Quantum systems suggested as QC

Requirements for a Quantum Requirements for a Quantum ComputerComputer

(1)Qubit :two quantum states with good quantum

#(2) Read : Detection(3) Single qubit operation (addressible)(4) Interaction (controllable) :

well defined and on-off(5) Coherence : isolation from

environment (6) Scalability

Photon

Quantum dot

Josephson

NMR

Ion trap

Si-base QC

Qubit 0 …. 5 …. 10 … 20 …..100

2007.11

Pra

ctic

al Q

uan

tum

co

mpu

ter

Si-based QC (Kane model)

SiP

electrodeinsulator

rf coil magnet

Si-based QC (Kane model)

SiP

• Qubit : nuclear spin of P• Coherence time at 1.5 K

el. spin ~ 103 Sn. spin ~ 10 h

• Silicon technology

Qubit

Read

Addressing

Interaction

Coherence

Scalability

Qubit

Read

Addressing

Interaction

Coherence

Scalability

Si-based QC (Kane model)

H

rf coil magnet

?

?

rf coil magnet

Single qubit operation (addressing)-hyperfine interaction engineering

H

Htotal = Hext+Hhyp

Use electric field to change Hhyp

Single qubit operation (addressing)-hyperfine interaction engineering

rf coil

P atom

B. Kane, Nature 393, 133 (1998)

++

Interaction control- RKKY interaction engineering

10nm

electrode

arXiv:cond-mat/0104569

Australian Work

Kane Model

P doped Silicon

Single spin detection (SET, MRFM)

Ensemble detection (NMR)

Our strategy

Verification of Kane’s QC model

• 1st step– Detection of P NMR signal

• 2nd step– Hyperfine interaction control by E

field

• 3rd step– RKKY interaction control by E field

1st step of Verification of Kane’s QC

• Detection of P NMR signal - never done– Fix fluctuating electron spin by low T

and high H to sharpen spectrum.rf coilH

Htotal = Hext+Hhyp

0phH

frequency

0 .( )ph H FH H

Low HHigh T

High HLow T

ExperimentExperiment

• P NMR of

Si:P with n ~ 1x1017 /cm3

Temp : 45 mK ~ 3.5 K

Field : 7.3 Tesla

3He/4He Dilution Refrigerator(Low Temperature Physics Lab. Kyoto Univ. )

No signal yet

Hex

He

Hex

He

E field

HexHex

HeHn

0phH

frequency

0 .( )ph H FH H 0 .( )ph H FH H

0E

0E

0phH

frequency

0 .( )ph H FH H

NMR - Direct Approach

Electrical control of NMR frequency

Hhyp

Alternative Approach - ESR

Hhf

Quantum Information Science

• Developing a practical quantum computer is the key issue.

• We are on a normal research track after the initial excitement.

• Development goes with nanotechnology.

• Eventually we will get it!

The

ENDThe

END

• Detection of frequency shift frequency shift by E field– hyperfine interaction control

rf coil

2nd step of Verification of Kane2nd step of Verification of Kane’’s QCs QC

H

• Spectral shape changeSpectral shape change by electric field– RKKY interaction control

rf coil

3rd step of Verification of Kane3rd step of Verification of Kane’’s QCs QC

ENDOR- Sample concentration < 1×1016/cm3

- Temperature < 4K

- Magnetic field T~3.3KG and frequency~9GHz

RF frequency

0E 0E

. 0( )ph H FH H . 0( )ph H FH H

We can check NMR

frequency shift by ENDOR