basic principles of quantum computing i
DESCRIPTION
Basic Principles of Quantum computing I. Soonchil Lee Dept. of physics, KAIST. 양자전산의 중요성. 1 MIPS 컴퓨터로 10 16 개의 자료 중 하나를 찾을 때 고전컴퓨터 : 300 년 양자컴퓨터 : 1 분 현대 암호는 모두 NSA 에서 개발 양자전산 개발을 늦추면 암호종속 모든 정보의 일방적 유출. Classical computing. Quantum computing. INPUT. OUTPUT. GATE. - PowerPoint PPT PresentationTRANSCRIPT
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Basic Principles of Quantum computing I
Soonchil LeeDept. of physics, KAIST
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• 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
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Quantum computingQuantum computing
/0 iHt
i Ht
e
OUTPUT U INPUT
Classical computingClassical computing
INPUT OUTPUT
GATE
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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
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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
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Classical computingClassical computing
INPUT OUTPUT
GATE Ex) ADDER
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Quantum computingQuantum computing
INPUT OUTPUT
GATE Ex)
U1 U2 U3
t
U1
U2
U3
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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.
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0
0
dL
dt
M H
L H
0H
Single qubit operation
H
M
|1>
|0>
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* 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.
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* 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.
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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
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5 4 3 2 1 3
f(x)=0Classical computing
|1>+|2>+|3>+….
f(x)=0
|3>
Quantum computing
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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
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• 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
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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
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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
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(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
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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
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(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
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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
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Magnetic Resonance Force Microscopy (MRFM)
- Scanning Probe 와 공명의 결합
- 단일스핀 감지
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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
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Ion trapIon trap
Qubit - ion spin stateSingle spin operation - laserInertaction - vibration(CM motion)
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Environment
measurementfield
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Basic Principles of Quantum Basic Principles of Quantum computing IIcomputing II
Soonchil LeeDept. of physics, KAIST
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10 years ago…
• 1st demonstration of quantum computing by NMR
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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.
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Things change. Now…
• Developing a Practical Quantum Computer is the key issue.
TheoryExperiment
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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
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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
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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
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Si-based QC (Kane model)
SiP
electrodeinsulator
rf coil magnet
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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
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Qubit
Read
Addressing
Interaction
Coherence
Scalability
Si-based QC (Kane model)
H
rf coil magnet
?
?
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rf coil magnet
Single qubit operation (addressing)-hyperfine interaction engineering
H
Htotal = Hext+Hhyp
Use electric field to change Hhyp
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Single qubit operation (addressing)-hyperfine interaction engineering
rf coil
P atom
B. Kane, Nature 393, 133 (1998)
++
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Interaction control- RKKY interaction engineering
10nm
electrode
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arXiv:cond-mat/0104569
Australian Work
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Kane Model
P doped Silicon
Single spin detection (SET, MRFM)
Ensemble detection (NMR)
Our strategy
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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
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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
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0phH
frequency
0 .( )ph H FH H
Low HHigh T
High HLow T
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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. )
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No signal yet
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Hex
He
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Hex
He
E field
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HexHex
HeHn
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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
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Alternative Approach - ESR
Hhf
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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!
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The
ENDThe
END
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• 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
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• 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
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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