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

Motivation

Shor Algorithm for prime factorization: killer application

Error correction on a QC is possible

Peter ShorR. Feynman

Charles

Bennett

David

Deutsch

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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'(

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#

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=""#

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'(

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'(""#

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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

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 >>

?

Quantum Dot Architectures

GaAs/

AlGaAs

Si/SiGe

Carbon Nanotubes

Ge Huts

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]

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

- -- - - -- - - -- - - -

- - -

- - -

-

- - -

-

Metal

gates

-V (volts)

single electron

wave function

Goal: a single electron tunably confined vertically and

horizontally in a semiconductor nanostructure

20-100 nm

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

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!

!

Entanglement

A quantum state of N qubits that cannot be written as a N-tensor

product is said to be entangled.

21??

2

1100!"

+=#

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

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

!!"

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&=

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.

Initialization Schemes

• B-field

• Neighbor reference spin

• Optical pumping

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

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

cgtahan@wisc.edu