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Experimental and theoretical studies of
semiconductor quantum bits
양자정보처리연구단
iQUIPS
Doyeol Ahn
Institute of Quantum Information
Processing & Systems
University of Seoul
Collaborators
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




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
Further Acknowledgements
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This work is supported by the Korean Ministry of Science and
Technology through the Creative research Initiatives Program under
Contract No. M10116000008-02F0000-00610.
Motivation
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
Solid state quantum bits:


Decoherence control in charge qubit




Spin vs Charge qubits
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)



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Understand and implement semiconductor
quantum bits (spin vs. charge qubit)
Understand
decoherence
processes
(nonMarkovian domain)
Fundamentals of Quantum Entanglement
Quantum Information Theory
What is quantum information processing?
iQUIPS

A research in quantum information processing is to understand
how quantum mechanics can improve acquisition,
transmission and processing of information.
Who may be involved?

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Computer scientists
Mathematicians
Electrical engineers
Chemists
Physicists
양자 상태 vector를 source로 하는 경우

Qubit: a vector in Hilbert space
"0" "0" ei  0
"1" "1" ei  1

Superposition
  C0 0  C1 1
2
 |0> with prob. |C0|
2
 |1> with prob. |C1|
 {|0>, |1>} = H2
 Vectors in 2-D Hilbert space
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Tensor product
1  1 
0  | 0      
 0  0
1 
 
0


0
 
0
 0  1 
1  | 0      
1   0 
0
 
0


1 
 
0
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1   0 
0  | 1      
 0  1 
0
 
1


0
 
0
0
 
 0  0  0
1  | 1       
1  1   0 
 
1 
Deutch Problem : quantum parallelism (1)
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Black
x
f (0)  f (1)
box
f(x)
: constant
f (0)  f (1)
: balanced
uˆ f : x y  x y  f x 
Se
t
uˆ f x
y 
1
2
1
0  1 
2
0
 1
x
0  f x   1  f x 
1
 0  f x   1  f x  
2
 0  1 if

 1  0 if
  1
f x 
0
f ( x)  0
f ( x)  1
1

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Example : f (0)  1, f (1)  0
0
1 
uˆ f : 0  0  0  0  f  0  | 0 |1   
0
 
0
1 
0
uˆ f : 0  1  0  1  f  0  | 0 | 0   
0
 
0
Deutch Problem : quantum parallelism (2)
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 uˆ f x
1
 0  1   x  1 f  x  1  0  1 
2
2
Set
uˆ f :
x 
1
0  1
2

1
0  1  1 0  1 
2
2

1
f 0  1
 0  1   1 1  1 f 1 1  0  1 
0  1
2
2
2
2

1
 1 f 0  0   1 f 1 1
2

 12  0
1

 Output f(0)&f(1) can be calculated at the same time!!!
Deutch Problem : quantum parallelism (3)
û f
uˆ f x 0  x f x 
on N qubits
Set
 1

 2
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 0  1 

 1

uˆ f 
0  1
 2

N
2 N 1
1

2
N
0  uˆ f


N
2
x 0
2 N 1
1
N
2
1
2
 Massive parallelism !!!
(2N outputs in one query)
x
N
2

x 0
x 0
2 N 1
 x f x 
2 x 0
A Quantum Information Science and technology
Roadmap
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Chrage qubit
(NTT)
Chrage qubit
(iQUIPS)
Cooper pair qubit
(NEC)
Cooper pair CNOT
(NEC)
Real operation in time domain
Design and fabrication of hybrid circuits
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
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)
Fabrication and characterization of a vertical QDT
for quantum gate operation
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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.
3.0x10
11
2.5x10
11
2.0x10
11
1.5x10
11
1.0x10
11
5.0x10
10
2
Current Density [A/cm ]
top electrode
circuit for the
generation
of local B
pillar
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Applied Voltage [eV]
-0.040
f-state
Stacked QD
0.3
0.2
Single QD
0.1
-0.056
Energy (eV)
dI/dV (S)
dI/dV (S)
AS
0.4
0.4
0.0
S
0.5
B = 0 T, T=20 mK
0.5
AS
symmetric : S
anti-symmetric : AS
0.3
0.2
0.1
d-state
-0.058
S
AS-Py
-0.180
-0.181
-0.182
-0.183
-0.184
-0.185
AS-Px
p-state
-0.362
0.08
0.10
0.12
V (V)
0.14
0.08
0.09
0.10
V (V)
S-Py
S-Px
AS
0.11
-0.364
s-state
S
-0.366
0
2
4
6
8
10
B (T)
12
14
16
18
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Simple spin dynamics for 1-qubit (interaction picture)
H     B, B  B0 zˆ  B1 ( xˆ cos t  yˆ sin t )
 (0 / 2) z  g ( x cos t   y sin t )
| (t )  exp(i z t / 2) |  (t )

|  (t )  H |  (t )
t

  

 i | (t )   0
 z  g x  | (t )
t
 2

i
  
 
 | (t )  exp i  0
 z  g x  t  | (0)
 
 2
= exp i nˆ   / 2 | (0) ; single qubit rotation about nˆ axis
when   0  nˆ  zˆ and 0    nˆ  xˆ
  t (0   )2  4 g 2
Fabrication of nano-electromagnet for quantum gate
operation
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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.
12
<Vin> = 1.1 ~ 6 mV (100 nm spacing)
<Vin> = 1.0 ~ 5 mV (11 m spacing)
10
<I2> (nA)

8
6
4
2
0
0
200
400
600
f (Hz)
800 1000
Realization of a charge qubit using stacked InAs selfassembled quantum dots #1
0.0
T=4K
8
-0.2
-0.4
-0.6
-0.8
6
AS
4
S
2
dI/dV (S)
Isub
5 nm GaAs
InAs QD
5 nm GaAs
InAs QD
6 nm GaAs
0.6 m GaAs
buffer (1018)
n+ GaAs
sub
I (A)

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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.
0
-1.0
-2
-0.9 -0.8 -0.7 -0.6 -0.5
V (V)
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
Evolution of a quantum state
 |  (t ) 
i
 H (t ) |  (t ) 
t
6
|  (t )   S k (t ) exp  i k t / | k 
k 0
S o (0)  1
S k (0)  0
(k  1,2,3,4,5,6)
Realization of a charge qubit using stacked InAs selfassembled quantum dots #2
0.00
-0.01
-0.02
100
0.04
Isub (pA)
-0.8
-0.6
Veff (V)
C
-5
-10
0.5
A
B
D
0.0
-15
-0.5
-20
-1.0
0
100 200 300 400 500
 t (psec)
dIsub/d(t) (Arb. unit)
0
150
-0.02
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
300
310 320
t (ps)
330
340
(c) 4 K
350
360
0.2
0.1
0.0
-0.1
-0.2
290
370
380
t (ps)
390
400
(d) 88 K
Isub (pA)
1.0
140
0.00
0.08
0.04
0.00
-0.04
-0.08
-0.12
300
310
320
t (ps)
330
340
(e)
Isub (pA)
-1.0
130
t (ps)
(b) 4 K
-0.04
290
-1.6
120
4K
360
380
400
t (ps)
420
440
3
2
1
0
0
100 200 300 400
Frequency (GHz)
500
100 200 300 400
Frequency (GHz)
500
100 200 300 400
Frequency (GHz)
500
100 200 300 400
Frequency (GHz)
500
100 200 300 400
Frequency (GHz)
500
6
4
2
0
0
8
6
4
2
0
0
1.5
1.0
0.5
0.0
0
Amplitude (arb. unit)
-1.2
0.02
110
Amplitude (arb. unit)
-0.8
Isub (pA)
(a) 4 K
Amplitude (arb. unit)
100ps
Isub (pA)
Isub (pA)
-0.4
0.01
Amplitude (arb. unit)
Isub (pA)
0.02
Amplitude (arb. unit)
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5
4
3
2
1
0
0
Direct measurement of tunneling rate through InAs
self-assembled quantum dots #1
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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 timedomain transport measurements.



D
Drain
S
QD
-1.1
Source
25
 from 1 to 0
21
18
-1.3
15
-1.4
12
C
A
B
C
-1.5
-0.29
B
-0.28
V(V)
dI/dV (nS)
I (nA)
-1.2
20
dI/dV (nS)
S
D
15
10
A
9
-0.27
-0.29
-0.28
VDC (V)
-0.27
Direct measurement of tunneling rate through InAs
self-assembled quantum dots #2
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High Frequency (50 MHz to 2 GHz)
1.0
0.6
dI/dV

0.8
Experiment
Fit
0.4
0.2
0
4
8
12 16
1/f (ns)
20
24
28
DC
-0.29
-0.28
VDC(V)
-0.27
Evidence of double layer quantum dot formation in
SOI QDT
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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.
VGS
CGS1
CGS2
VDS
CD1
CD2
Cm
QD 1
QD 2
CS1
CS2
CBS1
CBS2
VBS
10
VGS(V)
0.60
VDS(mV)

0
0.55
-10
0.50
0.55
VGS(V)
0.60
-50
0
VDS(mV)
50
New proposal for Si quantum dot qubit and quantum
gate
iQUIPS

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.
0.1
E (valley 5,6)
5
E (valley 1,2)
E (valley 3,4)
4
2
0.08
E (valley 1,2)
E (valley 5,6)
1
3
D
Energy (eV)
0.06
E
E (valley 5,6)
5
0
E
3
0.04
Anti-symmetri c
state
C
0.02
Symmetric
state
0
0
D. Ahn, J. Appl. Phys. 98, 033709 (2005)
100
200
300
Electric Field (kV/cm)
400
500
iQUIPS

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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Electron state in a quantum dot

 

F (r )  
F (k ) exp( ik  r )

k
,
F(k )   i Fi (k )
i
i : expansion coefficient for the valley i (group Td )
iQUIPS
 i (k ) Fi (k )   Dkij,k nV (k  k n) Fj (k n)   Fi (k )
j
kn
Dkkij n  DKiji  , K j  n
D
ij
Ki , K j
 

 Ki
ij
Ki , K j
D
  n

 Kj
DKij i , K j
 I ij    J ij   n J ij n
 H l (i)  V (r )  E  Fl (r )   H


l ' l
ll '
(r , i) Fl ' (r )  0
iQUIPS
H
ll'
(r, i)
 Ill' exp[i(Kl  Kl' )  r ](V(r ))
i(Jll' ) exp[i(Kl  K l' ) r ](V (r ))
 exp[i(Kl  Kl' ) r ](V(r ))(iJ
ll'
 )
iQUIPS
ll'
Kl ,K l'
D
13
(K,0,0), (0,K, 0)
D
 Ill'  el el '  
12
(K,0, 0),( K,0,0 )
 0.3915, D
 0.2171
1
1
Ill'  (1 el el' )  (1  el  el ' )cos(2 K )
2
2
iQUIPS

Jll' 
Ill'
Kl

 el
Ill'
K
K
 el (1  el  el' )
sin( 2 K )
K
iQUIPS
0.15
Energy
|1>
B (operation)
E
E~
o
0.1
|0>
Energy (meV)
Field
E
A (preparation)
0.05

0
0
100
200
300
Electric Field (kV/cm)
400
500
iQUIPS
0.1
E (valley 5,6)
5
E (valley 1,2)
E (valley 3,4)
4
2
0.08
Anti-crossing Energies
(Point D of figure 3)
0.092
E (valley 1,2)
E (valley 5,6)
1
3
D
0.0918
E
E (valley 5,6)
5
0
Energy (eV)
Energy (eV)
0.06
E
3
0.04
Anti-symmetric
state
E anti-symmetric
5
0.0916
E: prepartion and read-out
E symmetric
5
F: operation
E anti-symmetric
3
C
0.0914
E symmetric
3
0.02
0.0912
Symmetric
state
126
128
130
Electric Field (kV/cm)
0
0
100
200
300
Electric Field (kV/cm)
400
500
132
134
iQUIPS
S , A
1 1


  S , A (r )   S , A S , A (r )

2   1
  1 
  2 
1 †
2
T12   dr1 dr2 a * (r1 ) H T (r1 , r2 ) b (r2 )(  a )  b
iQUIPS
 




Vif   dr1 dr2 1 * (r1 ) 2 * (r2 ) 21   2 * (r1 )1 * (r2 )12 
 


 Vsc (r1  r2 )1 (r1 ) 2 (r2 )
 21  12 1
when electrons in dot 1 and dot 2 have same parity
 21  1 and 12  0
when 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
iQUIPS
25
20
20
15
15
10
10
Coulomb Energy (
eV)
25
5
5
0
0
0
100
200
300
Electric Field (kV/cm)
400
500
iQUIPS
 E11
 0
Hˆ  
 0

 0
0
E10
EC
0
0
Ec
E 01
0
0 
0 
0 

E 00 
Uˆ  exp(iHˆ t)




 exp(3it) | 1111|  cos 1t  i
sin  2 t|1010 |  | 0101| 

2




 exp(it) | 0000 | cos 3 t  1  i
sin  2 t| 1001 |  | 0110 | ,

2

iQUIPS
Swap Operation


|10  (cos1t i
sin  2t ) |10  (1  cos3 t  i
sin 2 t) | 01
2
2
for
t   /(2 3 )
  (4  13)
1 
| 10   | 01
|10   | 01  cos
2 2 
iQUIPS
Electron-phonon interactions in a Si dot
2

W 

2


q
1 1
2
 iq  r
2
 
E
(
N

)
|

f
|
e
|
i

|
 ( E f  Ei  q )

ac
q

2Vq
2 2
f
q
iQUIPS
10
1
Decoherence time (sec)
0.1
0.01
100 mK
0.001
0.0001
150 mK
10
10
10
-5
-6
-7
0
50
100
Energy ( 10
150
-6
eV)
200
250
Possibility of quantum gate formation by molecular
transistors
iQUIPS
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 .4
DS
V B G = 0 .2 V
0 .2
0 .0
V B G = - 0 .2 V
- 0 .2
- 0 .1 0
- 0 .0 5
0 .0 0
0 .0 5
0 .1 0
V D S(V )
30
T = 4.2 K
25
ID(pA)
I (n A )

V DS = 14 mV
 V BG = 112 mV
20
15
10
5
0
-0.3
V DS = 2 mV
-0.2
-0.1
0.0
VBG(V)
0.1
0.2
0.3
Possibility of quantum gate formation by DNA
molecules
iQUIPS
Thiol-modified double strand DNA molecules were shown to be selfassembled in the nano-gap with the help of Au nanoparticle. This opens up
a reliable fabrication of QDT with DNA molecules.
400
300
600
Thiol modified DNA+20 nm gold nanoparticles
Temperature=300 K
500
200
300
0
-100
200
-200
100
-300
0
-2
-1
0
V (V)
1
2
dI/dV (nS)
400
100
I (nA)

Doping of DNA molecules
iQUIPS
DNA molecules are found to be doped with Au atoms. Doped DNA
exhibits conductivity which is a strong function of the doping density.
40
30
Temperature = 300 K
Number of Base Pairs = ~2000
20
I(nA)

10
0
-10
Au Doped DNA
Undoped DNA
-20
-30
-3
-2
-1
0
V(V)
1
2
3
What are grand challenges in quantum information
processing?
iQUIPS





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.
iQUIPS