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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 Presentation
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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