spintronics and spin-based quantum dot quantum computingspin-based quantum dot quantum computing...
TRANSCRIPT
-
Spintronics
and
Spin-based
quantum dot
quantum computing
Charles Tahan
Physics Dept., University of Wisconsin-Madison
ECE746-Quantum Electronics, Guest Lecture
2:30pm, Oct. 26, 2004
-
Ahead of the curve
Spintronics
Quantum dot quantum computing
Datta/Das SPINFET paper
Loss/Divincenzo paper
QDQC in silicon at Wisconsin
-
Datta/Das: “Electric analog of the optoelectronic modulator”
Schotkky gate
AlAs
InAs
Ferromagnetic
sourceFerromagnetic
drain
quantum
wire
• Ballistic electron transport through the quantum wire
• Spin polarized injection from ferromagnetic source
• Spin orbit coupling rotates the electron spin depending on
the strength of the electric field and the length of the wire
• At the drain, the electron’s transmission probability depends
on the relative spin alignment
• Thus control of the source-to-drain current with the top gate
• a SPINFET?!
B = v "E
-
Mark Eriksson (Physics)
Robert Blick (ECE)
Sue Coppersmith (Physics)
Robert Joynt (Physics)
Max Lagally (Materials Science)
Dan van der Weide (ECE)
Mark Friesen (Materials Science and Physics)
Don Savage (Materials Science)
Levente Klein (Physics)
Shaolin Liao (Materials Science)
Keith Slinker (Physics)
Charles Tahan (Physics)
Jim Truitt (ECE)
Kristin Morgenstern (Physics)
Srijit Goswami (Physics)
Diu Ngeihm (Physics)
UW-Madison Solid-State Quantum Computing
-
Quantum
Com
puting
Quantum Algorithms /
Computer Science,
Math
Quantum Devices /
Physics, ECE
Quantum Technology New paradigm for
information science
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Motivation
Shor Algorithm for prime factorization: killer application
Error correction on a QC is possible
Peter ShorR. Feynman
Charles
Bennett
David
Deutsch
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Quantum over classical
• Superposition - Parallelism
• Interference
• Entanglement
-
Building a QC
• Good, scalable qubit
• Two-qubit entanglement operation
• Fast readout/measurement of qubit
• Fast initialization / source of new qubits
• Quantum error correction
• Flying qubits
-
Formalism
!!"
#$$%
&=0
10 !!
"
#$$%
&=1
01Qubit:
“off” “on”
!!"
#$$%
&
±=
±=±
1
1
2
1
2
10
“off AND on”
Quantum superposition
Multiple qubits:
[ ]180
1
0
0
1
0
0
1
1
00
1
01
0
1
1
0
0
1
010
!=""#
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=((
dimensional
Hilbert
space
-
Formalism
Density matrix formalism
State vector formalism of quantum mechanics
!! EH =
!=i
iiip ""#[ ]!! ,Hi
h& "=
!!"
#$$%
&=
00
01
0' !!
"
#$$%
&=
10
00
1' !!
"
#$$%
&=
+11
11
2
1'
L!!!=321""""QC
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Good qubit: Spin• Electronic or nuclear spin !
• Natural 2 level system
• Long coherence times
• Scalable (?) in semiconductor structures
B
!!"
#$$%
&=
00
01
0' !!
"
#$$%
&=
10
00
1' !!
"
#$$%
&=
+11
11
2
1'
Example:
!!"
#$$%
&=
11
11
2
1' !!
"
#$$%
&=
10
01
2
1' !!
"
#$$%
&=
00
01'
0=t 21 TtT >> 1Tt >21 TT >>
?
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Quantum Dot Architectures
GaAs/
AlGaAs
Si/SiGe
Carbon Nanotubes
Ge Huts
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Wisconsin QDQC design
1. Gated Quantum Dot QC (Loss & DiVincenzo)
• 1 electron spin = 1 qubit
• Self aligning to gates (no need to align to donors)
• Fast operations through Heisenberg exchange
• Scalable (hopefully)
2. Silicon
• Long decoherence times (T2 ~ milliseconds for P:28Si)
• Low spin-orbit coupling
• Spin-zero nuclei 28Si
3. Back-gate
• Size-independent loading and well-screened
manipulation of dots[Freisen, et.al., APL]
[Freisen, et.al., PRB]
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A quantum well quantum dot
Si substrate
Step graded
Silicon-Germanium
Si0.75Ge0.25
Si0.75Ge0.25
Strained SiQuantum
Well
(6-12 nm)
Step graded SiGe
Si cap layer
Phosphorous donor atoms130 meV
z
- -- - - -- - - -- - - -
- - -
- - -
-
- - -
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Metal
gates
-V (volts)
single electron
wave function
Goal: a single electron tunably confined vertically and
horizontally in a semiconductor nanostructure
20-100 nm
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Details…
kx
ky
kz
strain
conduction band
~ 0.1 - 1 meV
> 1 meV
z (1
5 n
m Q
W)
Bloch functions
!
" = Envelope #Bloch
-
Si substrate
Graded
SiGe
Si0.75Ge0.25
Si0.75Ge0.25
Strained 28Si
Graded SiGe
Si cap layer
Phosphorous donor atoms
Metal
gates
V (volts)
single electron
wave function
1/f noise
Nuclear 29Si
spectral
diffusion
.N29
Donor
free (danger)
zone
Ge
impurities
in w.f. tail
Rashba
Spin-Orbit
Coupling
qubit-qubit
magnetic
dipole
coupling
Quantum
Well
(6-12 nm)
phonons
Decoherence
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Universal QCQuantum Algorithms /
Computer Science,
MathA universal set of gates can compute an arbitrary
function (e.g. NAND for classical computation)
Single qubit gates and CNOT are a universal set of gates for
quantum computation.
!!!!!
"
#
$$$$$
%
&
=
0100
1000
0010
0001
CNOTU
CN
OT!
!
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Entanglement
A quantum state of N qubits that cannot be written as a N-tensor
product is said to be entangled.
21??
2
1100!"
+=#
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Exchange and CNOT
J ! 0
Uncoupled
J > 0
Swap
H2 quantum dots " Heff = J s1!s2
SWAP: Int[J(t) dt] = #!
SWAP doesn’t entangle but
Sqrt[SWAP] does.
=> CNOT
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Simulation: Coupled Qubits in Silicon
on
off
screened
potential
unscreened
potential
(Friesen, Rugheimer, Savage, et al., ’03)
on
off
screened
potential
probability
density
J =20 µeV
J ! 0
-
Exchange and CNOT
Heff = J(t) s1!s2
SWAP
Zi
SWAP
ZiZi
CNOTUeUeeU 121
)2/()2/()2/( !!! "=
!
U(t)" = ei
hS1 #S2 J (t )$ dt
21
2
2
2
1
22 SSSSS !++=
!==" h/)( JTdttJ
SWAP
iiUeieU4/
1000
0120
0210
0001
exp21 !! ! =
"""""
#
$
%%%%%
&
'
(((((
)
*
+++++
,
-
.
.==
/SS
-
One qubit operations
• Single qubit rotations on the Bloch sphere
!!"
#$$%
&=
01
10X
!!"
#$$%
& '=
0
0
i
iY
!!"
#$$%
&
'=
10
01Z
!!"
#$$%
&
'=
11
11H
!!"
#$$%
&=
)4/exp(0
01
'iT
X
Y
Z
H
T
!! h/iHteU "=
2/XieU
!"=10 =X
2
100
+=H
Physical
realization?
• ESR-AC Magnetic
• On-chip Magnetic
• Neighbor
ferromagnetic dot
• encoded qubits
-
Encoded qubits
Logical qubit
L0
L1
01
10
Physical qubits
Doing a swap operation is the same
as an X operation on the encoded
space.
0110)2,1( == XUSWAP
Exchange is the same as rotation
about X axis.
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Initialization Schemes
• B-field
• Neighbor reference spin
• Optical pumping
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Readout Schemes
• Magnetic STM tip
• Spin-charge transduction
– Spin-blockade transport measurement
– Spin-orbital transduction
-
Device design for QD readout
• Spin-dependent
charge motion
• SET detection
• Microwave pumping
y2DEG
SET island
Quantum DotSchottky
gates
Fast readout and initialization is
important for error correction
[Friesen, Tahan, Joynt, Eriksson, condmat]
History…spin-charge
transduction
Loss/Divincenzo,
Kane, …
-
Charge movement in asymmetric well
relaxation
!
"
!
"microwave
induced
oscillations
• spin info to charge info via spin-
dependent excitation
B
Gate potentials define quantum well
y
-
QEC - Active
No cloning theorem: it is NOT possible to make a copy of an
unknown quantum state
The Shor code: 9 qubits
!
0
H
0
CN
OT
CN
OT
0
H
0
CN
OT
CN
OT
0
H
0
CN
OT
CN
OT
0
0
CN
OT
CN
OT
!!!="
+++="
L
L
11
00
11111
00000
=!
=!
L
L
phase flip code
bit flip code
Threshold theorem
-
QEC - Passive
• Decoherence Free Subspaces
• Encoded qubits
• Uses a symmetry of the problem
Example: Collective dephasing
Error:
11
00
!ie"
"
Encoding: ( )
( )10012
11
10012
10
i
iL
+!
"!
Relative phases
do not change
under collective
dephasing
-
K.Slinker/L.Klein
Experimental Progress
Si substrate
Si.95Ge.05
Si.90Ge.10
Pure Si
Quantum
Well
Si.80Ge.20
Si.80Ge.20
Si.85Ge.15
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The end
• Quantum dot quantum computing in silicon
• http://qc.physics.wisc.edu/ for more
information on this and all Wisconsin QC
Charles Tahan
University of Wisconsin-Madison