Towards quantum information processing with spins in siliconcs191/fa07/... · Thomas Schenkel Berkeley Lab C191, Nov. 20, 2007-1000 -500 0 500 1000 1500 2000 2500 3000 3500 4000 10-1

Berkeley LabThomas Schenkel C191, Nov. 20, 2007

Towards quantum information processing with spins in silicon

Thomas SchenkelAccelerator and Fusion Research DivisionLawrence Berkeley National Laboratory

[email protected]://www-ebit.lbl.gov/


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Evolution of computational power

?


Scaling of CMOS (complementary metal oxide semiconductor) transistors is projected to reach really,

really hard limits in speed and power dissipation by about 2020.

What’s next ?


“Information is physical”

Classical information• Bit: 0, 1

• can copy

• not time reversible

• Boolean logic

Quantum Information

Classical information

Quantum information• Qubit: two state quantum system in superposition of basis states

• can not copy

• time reversible

• parallelism through entanglement

⟩β+⟩α=ψ 1|0|

1

0

1

0


Wave-particle duality of C60 molecules

Wave superposition of “which path” states in double slits leads to interferenceParticle interaction of molecules with environment destroys interference,

(decoherence, and “classical” behavior)Quantum info processing requires the coherent superposition of N qubits !

WaveParticle


0. Why Quantum Computation ?• information storage capacity of N qubits ~2N

• quantum algorithms promise speedups• general paradigm of quantum information theory

1. Why in solids ? • promise of scalability to large N needed to beat classical computers and

including error correction overhead (N>10,000)2. Why in Silicon ?

• long coherence times for electron and nuclear spins of donor atoms in a silicon matrix

• device requirements converting with trends in classical silicon transistor technology

3. Walk through five DiVincenzo criteria for donor electron spins in Silicon

Why quantum computation with dopant spins in silicon ?


Why in solids?

Scalability -

Classical transistor scaling and quantum computer development converge


“Moore’s Law” (Gordon Moore, Intel)exponentially more, cheaper, faster and smaller transistors

More transistors made each year then raindrops fall on California

more cheaper


Moore’s Law of exponential speedup of silicon transistors: faster


smaller

LBNL’03


“Classical” transistor scaling is over (again)

• power crisis limits size scaling of Silicon FETs• all stops are out, frantic search for:

• new materials • for gates (work function tuned metals)• for gate dielectric (high – k, HfOx, beyond ultra-thin SiO2)• for interlayer dielectrics (low – k, air-polymer foams, …)• hetero-epitaxial III-V on Silicon • carbon nanotubes, Graphene, …

• new geometries• multi-gate (FinFET, TriFET, …)• vertical FETs

• new state variables other then charge to represent bits• spin• structural phase, …

• new physics level: classical (Newton/Maxwell) Quantum This is the most exciting time in computer hardware research since the

invention of the first transistor (the replacement of vacuum tubes 60 years ago)


• vastly abundant semiconductor that is “easy” to work with • SiO2 / Si interface has quite low defect density

• (≤1010 cm-2eV-1, but that’s still ~1 per 100 nm scale device)• very high degree of control over electrical properties• allows large scale integration• most importantly: long spin coherence times (> 1 ms)

• because it can be prepared as a nuclear spin free environment (pure 28Si)

• compared to other materials with specific advantages:• III-V’s, e. g., quantum dots in GaAs

• direct band gap for opto-electronic integration • very high quality 2DEGs• but: short coherence times, ~1 μs, due to nuclear spin flips

• diamond (e. g., NV defects): • larger band gap for high temperature operation • low spin orbit coupling• but difficult to make larger wafers, hard to dope, …

• electrons on liquid helium, endohedral C60, …

Why quantum computing in silicon ?


Donor electron spin qubits in silicon

P: [Ne].3s2.3p3

Si: [Ne].3s2.3p2

• 3p3 binding energy: 45 meV • 100% abundant isotope with I=1/2• 28Si matrix can be prepared with I=0

31P (“natural quantum dot”)


Qubits:electron and nuclear spins of donor atoms in silicon

• Long decoherence times-nuclear spin: >1 s-electron spin: tens of ms

• Bohr radius of bound, 3p electron of 31P in Si: ~2 nm

)12(

53.00

20

2

00

0

=

=

==

Si

o

effSi

effSi

Amm

qmh

mma

ε

ε

πεε

TEM image taken from S. Dunham, ‘03

SiO2

Si


donor spins in silicon: “natural quantum dots”

1. Well defined extendible qubit array – stable memory 2. Initialization in the “000…” state3. Long decoherence time (>104 operation time, to allow for error correction)4. Universal set of gate operations (not, cnot)5. Read-out: Single-quantum measurements (projective measurement)6. Efficient quantum communication (form, transmit and convert “flying

qubits”)

20 to 200 nm

Criteria for physical implementation of a quantum computer (DiVincenzo)


• 31P-qubit: gate controlled manipulation of single spins; nuclear spins store information, electron spins transfer information between neighboring qubits (J, exchange) and to nuclear spins (A=121.5 neV, hyperfine interaction) (http://www.lps.umd.edu/)

Solid state quantum computer scheme with 31P in 28Si (B. E. Kane, Nature 1998)


1. Well defined extendible qubit array – stable memory• Array of single donor atoms (P, As, Sb, Bi) in a silicon crystal matrix formed by

single ion implantation (or STM-H lithography)

2. Initialization in the “000…” state• polarization at low temperature (0.3 K), in strong magnet field (5 T), kT<<gμBB

3. Long decoherence time (>104 operation time, to allow for error correction)• T2=T1 in pure 28Si >10 s, limited by residual 29Si, and by gate, and interface effects

4. Universal set of gate operations• Not: ESR rotations, need local B or g control• CNOT: two qubit interaction via J, or dipolar coupling, or RKKY, or e- shuttling

5. Read-out (projective measurement)• Single shot, single spin readout, much faster then decoherence time• spin-to-charge conversion, spin dependent transport

Criteria for physical implementation of a quantum computer(DiVincenzo)


J. O'Brien, et al., Univ. New South Wales, Sydney

Qubit arrays bottom up: STM hydrogen lithography

• Desorption of H with low energy electrons (~10 eV) from the STM tip

• Advantage: atomic resolution

• Problems: encapsulation, dopant activation, device integration, surface chemistry sensitivity

Aharonov-Bohm ring of P atoms connected to pre-implanted contacts, and overgrown with Si on Si (100); TC. Shen, J. Tucker, et al., 2003

50 nm

41nm

10nm

65nm



A. Persaud, et al.,Nano Letters 5, 1087 (2005)

Single Ion Placement with Scanning Probe Alignment Goal: place single ions with nm resolution

in situ scanning probe image of an aFet3

array of 90 nm dots in PMMA from ion implantation with scanning probe alignment


FEI Strata 235 dual beam FIB at LBNL

etching oxide deposition Pt deposition


• SII-SPM setup connected to high vacuum beam line • scan range of target stage is 0.1 x 0.1 mm2

• probe tip can be moved across 1 mm field• piezo-cantilevers co. I. Rangelow, Kassel University• holes down to 2 – 5 nm diameters by FIB and TEM processing

Setup for Ion Implantation with Scanning Probe Alignment


Single Ion Impact Detection

via: • detection of secondary electrons • collection of induced charge (IBIC) in diode or Fet• detection of channel current change in Fet


Ion implant setup with scanning probe alignment and three ion sources

1. Low density plasma source for low ion charge states and molecular ions, e. g. 15N2

+, Ar[1to 3+], 1 to 15 keV2. ECR (Electron Cyclotron Resonance

Source), runs on 2.5 GHz micro waves for low to medium ion charge states, e. g. Sb [3 to10+], 3 to 150 keV

3. EBIT (Electron Beam Ion Trap) for medium to high ion charge states, e. g. Sb [4 to 40+], 10 to 500 keV

1800 2000 2200 2400 2600 28000

3000

6000

9000

sb 7kV 062106 1

Uextr=7.2 kV23+

12+86.4 keV

17+

inte

nsity

(arb

. uni

ts)

magnetic field (kG)


• Distribution of probabilities for implantation of ions where theimplantation probability is small (<<1) for each incident ion and the number of ion impacts is large (>>1)

• At average, one ion is implanted. The probability for two adjacent ion hits is 13%

Beat a Poissonian distribution of implanted ions


Single Ion Detection in Readout Transistors through impact induced mobility changes

channel implant: 123 Sbgate oxide

28Si epi layer

Me

LTO

N+ N+

n-poly gate

• single ion doping of transistor channels through detection of current transients from single ion impacts (dI~20 nA/ion in 2x2 µm aFets)

0 20 40 60 80 100 120 140 160 180 200-1.0

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al a

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itude

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. uni

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time (s)


Single Ion Detection in Readout Transistors through impact induced mobility changes

• room temperature measurements of ion induced current changes in 2x2 micron FETs• can improve single impact amplitude a lot with some cooling and smaller devices• Appl. Phys. Lett. 91, 193502 (2007)


Poly and Tungsten electrodes allow annealing post single ion implantation of readout transistors


• Error budget in donor qubit placement– Ion beam spot size

• <5 nm with nanotubes ?– Ion straggling

• ~1/ion mass• ~1/ion energy• ~1/ion charge state (*)

– Dopant diffusion during annealing• Dopant specific• P: interstitial mediated diffusion, oxidation enhanced segregation• As: mixed vacancy / interstitial diffusion• Sb: vacancy diffusion, oxidation retarded segregation• Bi: transient enhanced diffusion


Scattering kinematics favours implantation of heavy donors into Si

31P, 15 keV

121Sb, 32 keV

209Bi, 40 keV

• implantation into a depth of 25 nm is accompanied by a much narrower dopant distribution (less straggling) for dopants heavier then silicon• a straggling of 10 nm can be achieved with 120 keV Bi, or 15 keV P (SRIM estimates)• we'd like to reserve As for S/D contacts

80 nm

80 nm

80 nm

80 nm


0 50 100 150 200 250 300 350 4001E15

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SiNx 60 keV 2E11 cm-2, RTA: times 2 SiO2 60 keV, 4E11, 1000 C 10 s N2 as implanted, 60 keV 4E11 cm-2

60 keV, 31P, 2E11 cm-2, SiNx, RTA: 1000 C, 10 s, N2

31p-60kev-sinx0606-1

SRIM depth: 74 nm, dx=30 nmconcentration: 2E11*1E5=2E16 cm-3 background: ~4E15 cm-3

conc

entra

tion

(31P

/cm-3

)

depth (nm)

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31P in Si: OED and large straggling due to symmetrical scattering

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ier

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atio

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Si3N4 N3 1E11 P/cm2 60 keV 10 s SiO2 O3 1E11 P/cm2 60 keV 10 s


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10 nmSiO2

Sb 90keV-Sio2 N2 SIMS 0606

90 keV, 121Sb2E11 cm-2, 0 degree10 nm SiO2RTA: 1000 C, 10 s, N2as impl: x=36 nmRTA: 40 nm1.2E11

12

1 Sb

conc

entra

tion

(cm

-3)

depth (nm)

Sbasimpl as implanted Sb.rta RTA

Sb – Si, 90 keV fwhm ~45 nm after RTA, ave. depth ~40 nm, dose: 2E11 cm-2


Ultimate limit in dopant placement by ion implantation ?

• Straggling: •minimize with low energy and high Z, can get <5 nm

• Diffusion / Segregation• Sb stays put

• spot size for CNTs ~ 1 – 20 nm

few nm placement accuracy is possible !

(can also use <10 nm e-beam apertures in aFets, but CNT collimators would work on any unstructured sample, e. g. for NV-center arrays)Electron transport through a single CNT

Images from Lee Chow, Univ. Central Florida, • Appl. Phys. Lett. 91, 103101 (2007); tests with ions in progress


1. Well defined extendible qubit array – stable memory• Array of single donor atoms (P, As, Sb, Bi) in a silicon crystal matrix formed by single ion implantation (or

STM-H lithography)

2. Initialization in the “000…” state• polarization at low temperature, in strong magnet field, kT<<gμBB• kT (0.3 K) = 0.026 meV, gμBB (5 T) = 0.58 meV

3. Long decoherence time (>104 operation time, to allow for error correction)• T2=T1 in pure 28Si >10 s, limited by residual 29Si, and by gate, and interface effects






STM-H lithography)2. Initialization in the “000…” state

• polarization at low temperature (0.3 K), in strong magnet field (5 T), kT<<gμBB

3. Long decoherence time (>104 operation time, to allow for error correction)• T2=T1 in pure 28Si >10 s, limited by residual 29Si, and by gate, and interface

effects





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Sample A (Sb28Si 2*1010 anneal 60s at 1000C)Experiment: n||B, T = 6.2K

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R In

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MI= +5/2

(D)

First ESR data on 121Sb implanted 28Si epi layerswith thermal SiO2 barriers (co. S. Lyon et al.)

in collaboration with Steve Lyon, Princetonuse Sb due to P contamination in

commercial 28Si, at 5x1013 cm-3 level•T2=0.3 ms at 5 K (T1=10 ms), indication that electron spins are affected by coupling to the SiO2/Si interface •first step in optimization of pre-device structures by ensemble ESR


SiO2

Si

X interface charges

X oxide charges

X nuclear spins

What limits coherence of donor electron and nuclear spins ?


Red: theory deSousa, et al.Blue: data, Lyon, ItohGreen: data, Lyon & Schenkel

De-coherence times of donor electron spins in silicon:limits due to 29Si

10-5 10-4 10-3 10-2 10-1 10010-5

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P in 28Si crystalX

evidence for effect of strain in epi-layers-SiO

2 interface ?

practicalpurity limit~10 ppm

theory: red: deSousa/dasSarma, PRB '0360 ms, P, 29Si: 500 or 800 ppm ?(Lyon, 03) extrapol.3 ms, P, 28Si crystal, 500 ppm 29Si (Ager, Lyon, TS)0.3 ms, Sb, 500 ppm, Isonics (Lyon, TS), implant0.26 ms, P, 29Si: natural, 4.6 % (Itoh)0.23, P, natural, implanted,8K (Lyon, TS)2 μs, P, 29Si: 99% (Itoh, 04)

T2-29Si-content-0804

T1=T2 limit at 1 K

500 ppmIsonics, ~0.2 s

natural

T

M (

s)

29Si fraction


Surface effects on Sb donor electron spin coherence

1. Fluctuation of trapping-centers at the Si/SiO2 interface (weak)

2. Spin-flips of paramagnetic centers at the Si/SiO2 surface DOMINANT

3. Hydrogen nuclear spins at passivated Si-H surface (very small)

T2 limiting factors

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Appl. Phys. Lett. 88, 112101 (2006)Theory: R. de Sousa, arXiv:0705.4088


Nuclear spin induced spectral diffusion limits T2 for hydrogen terminated silicon surfaces – limit: T2≈0.2 s for d, and 25 nm deep donors

(Rogerio De Sousa)

• donor depth ~ donor spacing for top gate control• nuclear spin effects also for 27Al2O3 (I=5/2), and Si3

14N4 (I=1)• but no nuclear spin for (thermal) SiO2, where electronic defects can be less then one per device !• 29Si limit to T2 at 500 ppm (commercial) is ~0.1 s (spectral diffusion theory, deSousa & DasSarma)




• polarization at low temperature (0.3 K), in strong magnet field (5 T), kT<<gμBB3. Long decoherence time (>104 operation time, to allow for error correction)

• T2=T1 in pure 28Si >10 s, limited by residual 29Si, and by gate, and interface effects





Stark Tuning of Donor Spin Resonance: Proto A-Gate

28Si:121Sb

( ) 2gg E g EηΔ = ⋅ ⋅( ) 2

aa E a EηΔ = ⋅ ⋅

325 330 335 340 345 350 355

ES

R A

bsor

ptio

n

M agnetic F ie ld (m T)

MI = -5/2 -3/2 -1/2 +1/2 +3/2 +5/2

E-field121Sb nucleus:

ISb = 5/2

Experiments:- Lateral gates to apply field- Long, narrow gates to avoid microwave absorption - Measure echo phase shifts ⇒ donor resonance shift


, ηg = -1·10-5 (in μm2/V2)( ) 2gg E g EηΔ = ⋅ ⋅

( ) 2aa E a EηΔ = ⋅ ⋅ , ηa = -3.7·10-3 (in μm2/V2)

MI = -5/2 -3/2 -1/2 +1/2 +3/2 +5/2

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Gate Voltage (in Volts)

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_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Gate Voltage (in Volts)

microwave:

electric field:

Quadratic Stark Experiments:

• First demonstration of gate control of the coupling between donor electrons and nuclei• Bradbury et al., Phys. Rev. Lett. 97, 176404 (2006)


• encoding of logical qubits in three electron spins allows universal QC with J only (DiVincenzo & Whaley ’00), alleviating the need for single electron ESR, “just” pulsing gate electrodes


Degeneracy of Si conduction band edge leads to oscillations of donor wave functions and J coupling

C. J. Wellard et al., Phys. Rev. B 68, 195209 (2003)

The solid line shows Kohn-Luttinger wave function for a phosphorus donor electron in silicon, plotted along directions of high symmetry within the crystal. The dotted line shows an isotropic 1s hydrogenic wave function, with a Bohr radius of 20 Å.


Skinner, Davenport, and Kane, Phys. Rev. Lett. 90, 087901(2003)

“Hydrogenic spin quantum computing in silicon: a digital approach”


Donor electron spin qubit devices based on single spin rotations and magnetic dipolar coupling

• “always on” D can be tracked in 1 D arrays• residual J treated as error with re-focusing protocols•CNOT gate time ~0.1 ms, o. k. when T2 is optimized to > 1 s• promising for demonstration of basic logic in devices with ~10 qubits

R. deSousa et al., PRA 70, 052304 (2004)

Donor qubit Zeeman frequencies:

iii Bγω =





• T2=T1 in pure 28Si >10 s, limited by residual 29Si, and by gate, and interface effects4. Universal set of gate operations

• Not: ESR rotations, need local B or g control• CNOT: two qubit interaction via J, or dipolar coupling, or RKKY, or e- shuttling




• charging energy for electrons to hop onto island: Ec=e2/2C >> kT

• tunneling “resistance” R>>1/G=h/e2 = 26 kOhm

• need Ec ~ 10 kT for reliable operation

• LHe, 4 K, kT = 0.34 meV

• SET at room temperature: capacitance of island ~1aF, size smaller than 10 nm

Single electron transistor as a sensitive electrometer

•http://physicsweb.org/article/world/11/9/7


Gate

DrainSource

SET electrometer

P

• Gate control of single spins and read out through spin dependent charge transfer between 31P atoms (based on singlet-triplet splitting and exclusion principle)

• For two spins there are three symmetric (triplet ) states: ↑↑,↑↓+↓↑ , ↓↓and one anti-symmetric (singlet) state: ↑↓−↓↑

Electron transfer into D- state singlet only for anti-parallel spins (triplet is not bound)

P

20 to 100 nm

Basic building block to access the physics of the 31P qubit: Two 31P atoms aligned with control gates and SETs

Kane et al., PR B 61, 2961 (2000)


Si-SETs in SOI with 10 nm line widths

1X

350,000X


15 nm

30 nm

Silicon nanowire SETs - direct lithographic access to 15 nm wires in SOI without stress limited oxidation

-0.86-0.7

-0.54-20mV

-10mV-0mV

10mV20mV

-4.0

-3.0

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Vg (V)Vs-d

Coulomb Blockade (15nm wire)

ΔVg = 200mV =e/8aF

- 2

- 3

- 4

ΔVsd = 22mVC= 2e/22mV= 15aF

15 nm 30 nm

S. J. Park et al., J. Vac. Sci. Technol. B 22, 3115 (‘04)

• direct lithographic control at 10 nm level in Silicon by e-beam lithography and dry etching• SET islands and tunnel junctions form by dopant segregation during source-drain implant anneals• issue: electronic defects at SiO2/Si interface will affect decoherence of nearby donor spins


• injected spins will be (mostly) down, donor spins will be up or down• for in-up – donor-up: only triplets can form (until spins flip in scattering)• for in-up – donor-down: singlets will form 50% of the time, and triplets will form 50% of the time • Scattering contributions from neutral impurities has to be about comparable to all other scattering mechanisms• demonstrated for 108 spins by Ghosh, and Silsbee, (1992)

tri0

.constII

σ×≈Δ

↑↑

)2

(.constII

sitri

0

σ+σ×≈

Δ↓↑

213trisi cm104 −−×≥σ−σ

Single Spin Readout via Spin Dependent Transport in FET channel


Spin-Dependent Transport in FETs• Schematics of SDT in single-donor aFETs

Spin-polarized source carrier injection (by static B-field/ ferromagnetic contact)

Gate voltage controls on/off state of transistor 2DEG carrier density

epi-28Si wafers for improved decoherence times (host substrate nuclear spin=0)

Current level is monitored for spin-state detection

source-injected conduction electrons(n+, Arsenic doped)

Donor atom (Phosphorus, Arsenic, Antimony, Bismuth, Lithium, Te, …)

Donor electron (bounded at low T), spin-state controlled by ESR techniques


a) Schematic cross-section of an aFET. (b) Device placement and field orientations in the ESR microwave resonator. (c) Magnified view of an aFET chip.

- Cheuk C. Lo, et al., Appl. Phys.. Lett., in press arXiv:0710.5164

Electrical Detection of Electron Spin Resonance


3252 3302 3352 3402 3452 3502 3552 3602

Magnetic Field (G)

ED

MR

Inte

nsity

I=5/2 I=3/2 I=1/2 I=-1/2 I=-3/2 I=-5/22DEG

Gate

Source

Drain 121Sb (I=5/2)

1st Observation of Spin Dependent Transport by Electrical Detectionof Magnetic Resonance (EDMR) in fully functional transistors with maximum integration potential, formed in 28Si with implanted 121Sb donors. Signal from ~106 donors in a 20x160 µm device. From line width of 1 G, we can estimate T1>>100 ns. Test bed for spin physics and scaling !


Projective single spin measurements by Electrical Detection of Magnetic Resonance ?

1. Due to efficient spin exchange between conduction electrons and bound donor electrons, spin dependent scattering alone does not allow projective measurements of the donor electron spin state

2. Need ability to SWAP quantum information from the electron to the nuclear spin

3. Position of electron spin resonance lines depends on nuclear spin state through hyperfine coupling

4. Detecting the presence or absence of selected hyperfine lines in EDMR constitutes a quantum non-demolition measurement of the nuclear spin state

5. Requirements are optimized signal amplitudes and nuclear spin relaxation times >1 ms, longer then shot noise limited measurement times

6. Next stop: single spin measurements in 50 nm scale transistors

Four-level system of electron-nuclear spin degrees of freedom.

M. Sarovar, et al., arXiv:0711.2343


1. Well defined extendible qubit array – stable memory• Array of single donor atoms (P, As, Sb, Bi) in a silicon crystal matrix formed by single ion

implantation (or STM-H lithography)2. Initialization in the “000…” state


• T2=T1 in pure 28Si >10 s, limited by residual 29Si, and by gate, and interface effects4. Universal set of gate operations

• Not: ESR rotations, need local B or g control• CNOT: two qubit interaction via J, or dipolar coupling, or RKKY, or e- shuttling

5. Read-out (projective measurement)• Single shot, single spin readout, much faster then decoherence time• spin-to-charge conversion, spin dependent transport in single ion implanted transistors with

maximum integration potential



After we demonstrate single spin readout and two qubit gates, the next big challenge is integration into 1D and then 2D arrays with efficient on chip communication

(“flying qubits”)


1. Develop devices for single spin readout• Spin dependent transport in transistors

2. Develop a technique for qubit array formation • Single ion implantation with Scanning Probe

alignment

3. Process and materials studies for T2 optimization • Spin dynamics in pre-device structures

4. Demonstration of quantum logic• Formulate logic protocol by mapping of physical

interactions to qubit gates

Path to quantum logic demonstrations with donor electron spin qubits in silicon

• theory – fabrication – measurement collaboration between LBNL (T. Schenkel – PI), UC Berkeley (J. Bokor, B. Whaley), and Princeton University (S. Lyon, A. Tyryshkin)

Berkeley LabUC Berkeley

Princeton


Q-Spin-FET• Development of single spin

readout transistors for projective single spin measurements

• Randomly bulk doped natural silicon, 28Si crystals, and 28Si epi- layers• Spectral and instantaneous diffusion• T2≥60 ms at 5 K (Tyryshkin, et al., Phys. Rev. B 68, 193207 (2003))

• Randomly ion implanted 28Si epi- layers with gate dielectrics (SiO2, Si3N4, Si-H)• Interface charge trap and defect dynamics• T2≥2 ms at 5 K, T1≥15 ms at 5 K (Schenkel et al., Appl. Phys. Lett.

88, 112101 (2006))

• Randomly ion implanted 28Si epi- layers with dielectrics and gates• electrical control of hyperfine coupling

and g-factor (Stark shift tuning) (Bradbury, et al., Phys. Rev. Lett. 97, 176404 (2006))

Q-ICs

Accessing donor spin qubits in silicon-from bulk ensemble studies to quantum devices

• Integrated multi-qubit arraysq-logic demonstrations, …


Outlook

• Quantum computing is bound to revolutionize information technology

• We have just scratched the surface of silicon• Spins of donor electrons and nuclei are very promising

qubits with strong large scale integration potential

Documents

Towards quantum information processing with spins in siliconcs191/fa07/... · Thomas Schenkel Berkeley Lab C191, Nov. 20, 2007-1000 -500 0 500 1000 1500 2000 2500 3000 3500 4000 10-1