iQUIPS

양자정보처리연구단

Experimental and theoretical studies of semiconductor quantum bits

Doyeol AhnInstitute of Quantum Information

Processing & Systems

University of Seoul

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Collaborators

H. K. Kim, S. H. Hong, B. C. Kim, Y. S. Choi: Dept. of Electronics & Computer Eng., Korea Univ.

Dr. J. H. Oh, Dr. H. J. Lee, Dr. J. S. Hwang, Dr. M. H. Son, Y. H. Moon: iQUIPS, Univ. of Seoul

S. Seong, Prof. T. H. Park: School of Chemical Eng., Seoul National Univ.

S. K. Kwak, Prof. D. J. Ahn: Dept. of Chemical & Biochemical Eng., Korea Univ.

Special Thanks to Program committee of AWAD 2005

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Further AcknowledgementsFurther Acknowledgements

This work is supported by the Korean Ministry of Science and

Technology through the Creative research Initiatives Program under

Contract No. M10116000008-02F0000-00610.

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Motivation

Solid state quantum bits: Spin vs Charge qubits

Decoherence control in charge qubit Very short decoherence of compound

semiconductor quantum dots Suppression of optical phonon processes in Si

quantum dots Utilization of multi-valley interactions in Si

Birth of New Information Technology

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Research Objectives (1998-2007) Understand and implement semiconductor

quantum bits (spin vs. charge qubit) Understand decoherence processes (non-

Markovian domain) Fundamentals of Quantum Entanglement Quantum Information Theory

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What is quantum information processing?

A research in quantum information processing is to understand how quantum mechanics can improve acquisition, transmission and processing of information.

Who may be involved? Computer scientists Mathematicians Electrical engineers Chemists Physicists

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양자 상태 vector 를 source 로 하는 경우

Qubit: a vector in Hilbert space

Superposition

|0> with prob. |C0|2 |1> with prob. |C1|2

{|0>, |1>} = H2 Vectors in 2-D Hilbert space

0"0""0" ie

1"1""1" ie

10 10 CC

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1

1 1 00 | 0

0 0 0

0

0

1 0 10 |1

0 1 0

0

0

0 1 01 | 0

1 0 1

0

0

0 0 01 |1

1 1 0

1

Tensor product

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Deutch Problem : quantum parallelism (1)

x f(x)Black

box

)1()0( ff : constant )1()0( ff : balanced

xfyxyxu f :ˆ

Set

102

1y

102

1ˆ xu f xfxfx 10

2

1

xfxf 10

101

01

10

xf

if

if 0)( xf

1)( xf

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0

1ˆ : 0 0 0 0 0 | 0 |1

0

0

fu f

: (0) 1, (1) 0Example f f

1

0ˆ : 0 1 0 1 0 | 0 | 0

0

0

fu f

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Deutch Problem : quantum parallelism (2)

102

1110

2

1ˆ xf

f xxu

Set 102

1x

102

110

2

1:ˆ fu

102

111

2

110

2

110

2

1 10 ff

102

11101

2

1 10 ff

Output f(0)&f(1) can be calculated at the same time!!!

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Deutch Problem : quantum parallelism (3)

fu on N qubits

Set

xfxxu f 0ˆ

12

022

110

2

1N

xN

N

x

02

1ˆ010

2

1ˆ

12

02

N

xNf

N

f xuu

xfxN

xN

12

022

1

Massive parallelism !!!

(2N outputs in one query)

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A Quantum Information Science and technology Roadmap

Cooper pair qubit(NEC)

Chrage qubit(NTT)

Cooper pair CNOT (NEC)

Chrage qubit(iQUIPS)

Real operation in time domain

Cooper pair qubit(NEC)

Chrage qubit(NTT)

Cooper pair CNOT (NEC)

Chrage qubit(iQUIPS)

Real operation in time domain

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Design and fabrication of hybrid circuits

SOI quantum dot transistors and circuits have been successfully fabricated and tested. We are now in the stage of designing, fabricating, and testing those circuits. The more important factor is that we will need to see the quantum gate operation and we have to wait for the setup of dilution refrigerator in the third stage. (In collaboration with SNU ISRC)

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Fabrication and characterization of a vertical QDT for quantum gate operation

A vertical QDT was successfully fabricated. The key processes are formation of vertical pillar and planarization by polyimide for contact isolation. The QDT also can include InAs quantum dots.

c i r c u i t f o r t h e g e n e r a t i o no f l o c a l B

t o p e l e c t r o d e

p i l l a r

c i r c u i t f o r t h e g e n e r a t i o no f l o c a l B

t o p e l e c t r o d e

p i l l a r0.0 0.1 0.2 0.3 0.4 0.5 0.6

5.0x1010

1.0x1011

1.5x1011

2.0x1011

2.5x1011

3.0x1011

Applied Voltage [eV]

Cur

rent

Den

sity

[A

/cm

2 ]

- 0 . 0 5 8

- 0 . 0 5 6

- 0 . 0 4 0

f - s t a t e

d - s t a t e

A S

S

S

A S

s y m m e t r i c : Sa n t i - s y m m e t r i c : A S

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8

- 0 . 3 6 6

- 0 . 3 6 4

- 0 . 3 6 2

- 0 . 1 8 5- 0 . 1 8 4- 0 . 1 8 3- 0 . 1 8 2- 0 . 1 8 1- 0 . 1 8 0 A S - P y

S - P y

A S - P x

S - P x

A S

p - s t a t e

Ss - s t a t e

Ene

rgy

(eV

)B ( T )

0.08 0.10 0.12 0.140.0

0.1

0.2

0.3

0.4

0.5 B = 0 T, T=20 mK

Single QD

Stacked QD

dI/d

V (

S)

V (V)

0.08 0.09 0.10 0.11

0.1

0.2

0.3

0.4

0.5

dI/d

V (

S)

V (V)

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0 1

0

Simple spin dynamics for 1-qubit (interaction picture)

ˆ ˆˆ , ( cos sin )

( / 2) ( cos sin )

| ( ) exp( / 2) | ( )

| ( ) | ( )

| ( )

z x y

z

H B B B z B x t y t

g t t

t i t t

i t H tt

i tt

0

0

0 0

| ( )2

| ( ) exp | (0)2

ˆ ˆ =exp / 2 | (0) ; single qubit rotation about axis

ˆ ˆ ˆˆ when and

z x

z x

g t

t i g t

i n n

n z n x

2 20 ( ) 4t g

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Fabrication of nano-electromagnet for quantum gate operation

Nanometer size electromagnet is an important ingredient for the realization of qubits and quantum gates. An AC magnetic field around the quantum dot can rotate the spin of the electrons in the quantum dot. We successfully fabricated nano-electromagnet and demonstrated the operation by Faraday’s induction experiment.

0 200 400 600 800 1000

0

2

4

6

8

10

12 <V

in> = 1.1 ~ 6 mV (100 nm spacing)

<Vin> = 1.0 ~ 5 mV (11 m spacing)

<I 2>

(n

A)

f (Hz)

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Realization of a charge qubit using stacked InAs self-assembled quantum dots #1

A charge qubit has been realized utilizing the symmetric/anti-symmetric quantum states of stacked InAs self-assembled quantum dots. Short period (> 30 psec) electrical pulses were applied on the source electrode and time-averaged decay current was measured as a function of pulse width. The decay current exhibits periodic oscillations as a function of the pulse width and this is a direct evidence of the manipulation of the quantum state in time domain. Our achievement was before the first electrical measurement of charge qubit by Fujisawa.

5 nm GaAs

InAs QD

6 nm GaAs

0.6 m GaAsbuffer (1018)

n+ GaAssub

5 nm GaAs

InAs QD

Isub

-0.9 -0.8 -0.7 -0.6 -0.5-1.0

-0.8

-0.6

-0.4

-0.2

0.0

T = 4 K

ASS

V (V)

I (

A)

-2

0

2

4

6

8

dI/dV (S

)

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Evolution of a quantum state

)6,5,4,3,2,1(0)0(

1)0(

|/exp)()(|

)(|)()(|

6

0

kS

S

ktitSt

ttHt

ti

k

o

kkk

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Realization of a charge qubit using stacked InAs self-assembled quantum dots #2

0 100 200 300 400 5000

1

2

3

4

5

360 380 400 420 440-0.12-0.08-0.040.000.040.08

290 300 310 320 330 340-0.2-0.10.00.10.2

0 100 200 300 400 5000.0

0.5

1.0

1.5

100 110 120 130 140 150-0.02

-0.01

0.00

0.01

0.02

0 100 200 300 400 5000

1

2

3

0 100 200 300 400 5000

2

4

6

290 300 310 320 330 340-0.04

-0.02

0.00

0.02

0.04

350 360 370 380 390 400

-0.06-0.04-0.020.000.020.040.06

0 100 200 300 400 5000

2

4

6

8

Frequency (GHz)

Am

plit

ude

(arb

. uni

t)(e)

4 K

Isu

b (pA

)

t (ps)

(d) 88 K

Isu

b (pA

)

t (ps)

Frequency (GHz)

Am

plit

ude

(arb

. uni

t)

(a) 4 K

Isu

b (pA

)

t (ps)

Frequency (GHz)

Am

plit

ude

(arb

. uni

t)

Frequency (GHz)

Am

plit

ude

(arb

. uni

t)

(b) 4 K

Isu

b (pA

)

t (ps)

(c)4 K

Isu

b (pA

)

t (ps)

Frequency (GHz)

Am

plit

ude

(arb

. uni

t)

0 100 200 300 400 500

-20

-15

-10

-5

0

D

C

B

A

t (psec)

I sub (

pA)

-1.0

-0.5

0.0

0.5

1.0

dIsub /d(t) (Arb. unit)

-1.0 -0.8 -0.6

-1.6

-1.2

-0.8

-0.4100ps

I sub (

pA)

Veff

(V)

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Direct measurement of tunneling rate through InAs self-assembled quantum dots #1

The tunneling rate through InAs self-assembled quantum dots was measured again by the electrical pump and probe measurement. Microwave (MW) signal was combined with the DC bias and was applied on the diode with InAs self-assembled quantum dots. Non-adiabacity factor of the decay current as a function of the frequency of the MW signal gives the direct estimate of the tunneling rate through the quantum dot. This experiment is another important achievement in time-domain transport measurements.

-0.29 -0.28 -0.27-1.5

-1.4

-1.3

-1.2

-1.1

9

12

15

18

21

dI/dV (nS)

I (nA

)

V(V)

ABC

CBA

-0.29 -0.28 -0.27

10

15

20

25 from 1 to 0

dI/d

V (

nS)

VDC

(V)

SourceDrain QD

S

SD

D

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Direct measurement of tunneling rate through InAs self-assembled quantum dots #2

-0.29 -0.28 -0.27

High Frequency (50 M

Hz to 2 G

Hz)

DC

dI/

dV

VDC

(V)

0 4 8 12 16 20 24 28

0.2

0.4

0.6

0.8

1.0

1/f (ns)

Experiment Fit

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Evidence of double layer quantum dot formation in SOI QDT

SOI QDT with a thin silicon layer showed, for the first time, evidences of double quantum dot formation each at the front and the back interface. This double layer formation can be used to automatically fabricate coupled Si quantum dot by fabricating a single quantum dot.

0.50 0.55 0.60-10

0

10

VGS

(V)

VD

S(mV

)

VGS

VBS

VDS

QD 1 QD 2

CGS1 CGS2

CBS1

CD1 CD2

CS1 CS2

CBS2

Cm

0.55

0.60

-50 0 50

VG

S(V)

VDS

(mV)

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New proposal for Si quantum dot qubit and quantum gate

The multi-valley quantum state transitions in a Si quantum dot is studied as a possible candidate for a quantum bit with a long decoherence time. Qubits are the multi-valley symmetric and anti-symmetric orbitals. Evolution of these orbitals is controlled by an external electric field, which turns on and off the inter-valley interactions. Such silicon quantum dot transistors were already fabricated for the test of the proposal.

0

0.02

0.04

0.06

0.08

0.1

0 100 200 300 400 500

En

erg

y (

eV

)

Electric Field (kV/cm)

E0(valley 5,6)

E1 (valley 1,2)

E2 (valley 3,4)

E3 (valley 5,6)

E4 (valley 1,2)

E5 (valley 5,6)

Anti-symmetric state

Symmetric state

C

D

E5

E3

D. Ahn, J. Appl. Phys. 98, 033709 (2005)

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New proposal for Si quantum gate Inter-valley interactions Qubit: multi-valley symmetric and anti-symmetric states Control: external electric field Long decoherence time

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,

k

rkikFrF

)exp()()(

Electron state in a quantum dot

F(

k ) iFi(

k )

i

: expansion coefficient for the valley i (group )i dT

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, nn

, nn

, , ,

'

( ) ( ) ( n) ( n) ( )

n

n n

( ) ( ) ( ) (

i j

i j i j i j

iji i j ik k

j k

ij ijK Kkk

ij ij ijK K K K K K

i j

ij ij ij

l l ll

k F k D V k k F k F k

D D

D D DK K

I J J

H i V r E F r H r

'

'

, ) ( ) 0ll l

i F r

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H ll' (r , i

)

Ill' exp[ i(K l

K l' )

r ](V(r ))

i(J ll'

)exp[ i(

K l

K l' )

r ](V (r ))

exp[ i(K

l

K

l' )

r ](V(r ))( i

J

ll'

)

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D K l ,

K l'

ll' Ill' e l

e l '

D(K,0,0), (0,K, 0)13 0.3915, D(K,0, 0),( K,0,0 )

12 0.2171

Ill'

1

2(1

e l

e l' )

1

2(1

e l

e l ' )cos(2K )

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J ll'

K l

Ill'

e l

K

Ill'

e l(1

e l

e l' )

K

Ksin(2K )

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0

0.05

0.1

0.15

0 100 200 300 400 500

En

erg

y (

meV

)

Electric Field (kV/cm)

E

B (operation)

A (preparation)

Field

Energy

E~

|0>

|1>

Eo

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0

0.02

0.04

0.06

0.08

0.1

0 100 200 300 400 500

En

erg

y (

eV

)

Electric Field (kV/cm)

E0(valley 5,6)

E1 (valley 1,2)

E2 (valley 3,4)

E3 (valley 5,6)

E4 (valley 1,2)

E5 (valley 5,6)

Anti-symmetric state

Symmetric state

C

D

E5

E3

0.0912

0.0914

0.0916

0.0918

0.092

126 128 130 132 134

En

erg

y (

eV

)

Electric Field (kV/cm)

E3 symmetric

E3 anti-symmetric

E5 anti-symmetric

E5 symmetric

E: prepartion and read-out

F: operation

Anti-crossing Energies (Point D of figure 3)

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)()(1

1

2

1,,,, rr ASASASAS

2 †12

2211

12112 )()(),()(* babTa rrrHrrdrdT

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)( )( )(

)(*)(*)(*)(*

221121

12211221221121

rrrrV

rrrrrdrdV

sc

if

-

21 12 1when electrons in dot 1 and dot 2 have same parity

21 1 and 12 0when electrons 1 dot 1 and 2 have opposite parities, which are preserved

21 0 and 12 1

when electrons 1 dot 1 and 2 have opposite parities, which are both changed

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0

5

10

15

20

25

0

5

10

15

20

25

0 100 200 300 400 500

Co

ulo

mb

En

erg

y (

eV

)

Electric Field (kV/cm)

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00

01

10

11

000

00

00

000

ˆ

E

EE

EE

E

HC

c

ˆ U exp(i ˆ H t)

exp(3it) | 1111| cos1t i

2

sin2t

|1010 | | 0101|

exp( it) | 0000 | cos3t 1 i

2

sin2t

| 1001 | | 0110 | ,

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|10 (cos1t i

2

sin2t ) |10 ( 1 cos3t i2

sin 2t) | 01

t /(23 ) (4 13)

|10 | 01 cos1

22

| 10 | 01

Swap Operation

for

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)(||||)2

1

2

1(

2

2 22

2qif

rqi

f qq

qac EEiefN

V

qEW

Electron-phonon interactions in a Si dot

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10-7

10-6

10-5

0.0001

0.001

0.01

0.1

1

10

0 50 100 150 200 250

Deco

here

nce

tim

e (

sec)

Energy ( 10 -6 eV)

100 mK

150 mK

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Possibility of quantum gate formation by molecular transistors

Multi-qubit can be realized from specially designed molecules since the abundance of quantum states in molecules can be utilized for quantum computation. However, direct electrical contact to individual molecules is still a difficult task even though a few pioneering works exist with limited reliability. We developed a way of contacting molecules by capturing Au nanoparticles in nano-gap electrodes covered with self-assembled mono-layer (SAM). We used AC dielectrophoresis technique for the capture and a reliable and reproducible capture was successfully done.

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.30

5

10

15

20

25

30

VDS

= 2 mV

VDS

= 14 mVV

BG = 112 mV

T = 4.2 K

I D(p

A)

VBG

(V)

-0.10 -0.05 0.00 0.05 0.10

-0.2

0.0

0.2

0.4

VBG

= -0.2 V

VBG

= 0.2 V

I DS(n

A)

VDS

(V)

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Possibility of quantum gate formation by DNA molecules

Thiol-modified double strand DNA molecules were shown to be self-assembled in the nano-gap with the help of Au nanoparticle. This opens up a reliable fabrication of QDT with DNA molecules.

thiol modified DNA + Au nanoparticlethiol modified DNA + Au nanoparticle

-2 -1 0 1 2

-300

-200

-100

0

100

200

300

400

Thiol modified DNA+20 nm gold nanoparticlesTemperature=300 K

I (n

A)

V (V)

0

100

200

300

400

500

600

dI/d

V (

nS

)

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Doping of DNA molecules

DNA molecules are found to be doped with Au atoms. Doped DNA exhibits conductivity which is a strong function of the doping density.

-3 -2 -1 0 1 2 3

-30

-20

-10

0

10

20

30

40

Au Doped DNA Undoped DNA

Temperature = 300 KNumber of Base Pairs = ~2000

I(n

A)

V(V)

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To manufacture, manipulate and characterize arbitrary entangled systems.

To develop the fundamental theory of quantum entanglement.

To control decoherence and prove the scalability of quantum information processing.

To develop application of the few qubit quantum information processor.

To master quantum coherences and understand the quantum-classical boundary.

What are grand challenges in quantum information processing?

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