Quantum Information Storage in Solid State Systems

David P. PappasNational Institute of Standards & Technology

Boulder, CO

M. Vissers, Jeff Kline

Something... “took a Quantum Leap!” Misnomer?

E = mgh

= (60 kg) x (9.8 m/s2)x(0.1 m)

= 60 kg m2/s2

E ~ 60 Joules

0.1 meter

Equivalent of man jumping 0.000 000 000 000 000 001 meters high < millionth of an atom

Quantum leap

1

E = 10 electron-volts

1 eV =1.602 x 10-19 Joules

Quantum Leap - E ~ 1 x 10-18 Joules

Hydrogen atom energy levels

-13.6 eV

-3.4 eV2

n=1

n=2

3

• electron acts like a wave

• not measured

• electron acts like particle

• when measured

• at some position

=> Quantum Hydrogen

“Quantum Leap” ≡ fundamental change in paradigm

Classical Hydrogen

• electron charged particle

• accelerating e- loses energy

• spirals in

• atom collapses

+

-

Quantum mechanics is Nature’s calculator…very very fast

• Example – Self assembly of atoms into molecules

• Difficult for classical computer to simulate the simplest

molecule

• Can we turn situation around?

– make artificial atoms

– redefine rules=> system solves problem

Caffeine Ethanol Aspirin

R. Marx, A. F. Fahmy, J. M. Myers, W. Bermel, S. J. GlaserPhys. Rev. A 62, 012310-1-8 (2000)

BOC-(13C2-15N-2D -glycine)-fluoride

5 “qubit” moleculeNMR

Quantum Information

Quantum Computing

• Factor large numbers

• Simulate physical systems

• Search databases

Quantum Cryptography

Send messages securely

Alternative to public key

Detect eavesdroppers

• What is different about Quantum Information?

• How is it useful?

• Can we control it?

• Software

• Hardware

Classical Cryptography• Public key

Send public key =15

Alice Bob

EveEavesdropper needs to figure out 15=3x5 to decode :

10941738641570527421809707322040357612003732945449205990913842131476349984288934784717997257891267332497625752899781833797076537244027146743531593354333897=

102639592829741105772054196573991675900716567808038066803341933521790711307779 x106603488380168454820927220360012878679207958575989291522270608237193062808643

• 7 months to reduce this number into it’s two prime factors

Need faster factoring - Quantum Computing

Need code that can’t be eavesdropped - Quantum Cryptography

Send message back

Pick 2 private keys, 3 & 5Send public key 15=3 x 5

Use private keys to decode

Receive public key = 15

Encode data with public key

Send encrypted message back

Progress in Quantum Information• Quantum Computing

– Software

• Quantum error correction – Steane, Shor PRL (1996)

• Fault tolerant algorithms – Knill, Nature (2005)

– Hardware

• NMR quantum computers have reached 5 bits

– Grovers algorithm - Vandersypen APL (2000)

– Shor’s alorithm - Nature (2001)

• Ion traps – demonstrated factoring

– Semi-classical QFT – Wineland, Science (2005)

– Quantum error correction – Nature (2004)

– Six atom Schroedinger Cat State – Nature (2005)

• Linear optics gate with photons – Franson PRA (2001)

• Solid state qubits demonstrate 2 coupled qubits

• Quantum cryptography

– Demonstrated, tested

• Practical demos - Zeilinger Optics Expr. (2004)

• 1.45 km through Vienna sewer system

– Scaling up to commercial products Bank

City Hall

Quantum Computing software – Digital Logic

• One classical bit

50%

50%

Measure• Quantum bit (qubit)

“0”

“1”

1beior

ifa=b

0a

• 2 states

• 6 states

Quantum computing more possible states & intrinsically parallel

Classical computation:

Quantum computation:

n bits => 2n possible states

S1 =00…000S2 =00…001S3 =00…010 …

ClassicalGate f(x)

Output f(S1) f(S2)

2n computationsSpans all input states

...

010..00c

001..00b

000..00a

Quantumgate f(x)

1 computation operates on all states

measure

n bits

Outputstate

n qubits => possible states n22O

• Classical algorithm:

– N =8 Items (states):

– On average, need to search N/2 (=4) items to find

– : O(N)

• Quantum Algorithm:

– Compares all coefficients at the same time

Quantum Interference Speed up of unsorted data search

a b c d e f g h

a b c d e f g h

Grover’s Search Algorithm

F( ) =>change sign if matches

“diffusion” operator - reflect around average

Weights:

• Grover’s algorithms conducts search in O(N1/2) vs. O(N)

Quantum systems “recognize” solutions

classical database doesn’t gain for simple search

N operations to load!

Resources - NlogN amplitudes for algorithm

Cryptography key search algorithms can benefit greatly

– Shor’s algorithm factors numbers

• Quantum Fourier Transform:

• Exponential speedup of FT

• Used to find factors of numbers

– Crack public key encryptions

• Quantum algorithms take fundamentally different mindset!

Quantum problem solving is fast

Quantum Computing Hardware

Coupling• Initialize• Store• Interact• Measure

Systems:

Superconductors

Phase, charge, flux ~~~~~~~~~~

Semiconductor spin

Quantum dot

~~~~~~~~~

NMR

Neutral atoms

Ions

Photons

Lifetimes

NIST - Quantum computing with real atoms

• 9Be+ ions - MEMs RF traps

• Addressed with focused lasers

• Shuttle ions around

– Store

– interact

• Long lifetimes

• Challenge is scaling & interaction

– initialization

– operation

– measurement

Making artificial atoms1) Use Superconductors

1. Zero DC resistance

- PDG-conductor at AC

2. Complete diamagnetism

3. Macroscopic quantum effects

2) Make LC circuit

3) Add non-linearity to define energy levels

I

L C Inte

nsi

ty

frequency0

LC1

0

Quality factor:

0Q

Lifetime: 0

Q

Thin, non-linearjunction

& capacitor

0.0 0.1 0.2 0.3 0.4 0.5

2

4

6

8

10

12

14

16

Fre

qu

ency

(G

Hz)

Temperature (K)

What temperature & frequency?• Freeze out quasiparticles (unpaired e -) in the superconductor

• Excitation energy >> Thermal

• f = 2 – 10 GHz range

• Need high Q for long lifetimes ~ 10 6 gives s time constants

• Need enabling technology for low T operation

– 0.05 to 0.1 K!

Tk2 B0

K 1.0 ~10

TT C

04/19/23 17

• Adiabatic demagnetization refrigerattor (ADR)

• High Precision Devices – Louisville, CO

• Automated mag cycl & T PID

• Demonstrated T < 100 mK > 400 hr

• < 1 day turnaround

• Hold time > 12 hr @ 0.1 K w /2 coax

• Closed cycle dilution refrigerators (DR)

• Multiple vendors – Oxford, BlueFors ,

Cryomagnetics, HPD, Quantum Design …

• 20 mK base

• Continuous > 400 μW power - ~ 100 coax

• ~ 10 kW power for He compressor & electronics

Closed cycle plug & play refrigerators T< 0.1 K

NIST – Quantum computing with superconductors

• Al/AlOX junctions on Si wafers

– optical lithography

• ~ 1 m features

– standard processing

• Al wiring w/SiO2 dielectric

• Addressed with RF pulses, DC bias currents

• Couple qubits with capacitors

• Challenge

– Improve lifetimes

– Reduce decoherence

• Operate at 20 mK

– Expected to reduce thermal

– decoherence sources

Solid State Quantum Iinformation– Challenges

• Need many qubits – 10 ~ 100 (logical)

• Need long quantum coherence times ~ ms

• Need high measurement fidelity ~ 99%

– Superconducting Josephson junction “phase” qubits

• Operation

• Spectroscopy

– Materials

• Al ring w/weak link

“Josephson Junction”

• SiOx substrate, insulator

• Al0x tunnel barrier

• Identification of decoherence

• Improvements

How do you talk to a phase qubit?

RF in~ 5-10 GHz

current bias in

SQUIDMeas.

• Artificial atom - use radiation

• Apply bias to adjust frequency

• “Listen” with SQUID magnetometer

qubit junction

Fabrication – trilayer process (Al)

Si

a-SiOx

Al/a-AlOx/Al

MesaTunnelBarrier

Al

Al – superconductor, TC ~ 1 K

a-SiO2: amorphous SiO2 - substrate & insulation

Chemical vapor deposition

a – AlOx: amorphous Al2O3 + OH- - tunnel barrier

Self passivated oxide ~ 1.5 nm thick

Superconducting Josephson junction phase qubit principle

TunnelJunction~1.5 nm

Top superconductor

Bottom superconductor

Itop= 0

bot= 0ei

Cooper pairwavefunction

Josephsonrelations

e2V

)sin(II 0

• I depends on

• Voltage only when

phase is

changing

Electrical circuit model of Josephson junction

V I

=CJ

LJ ~1/cos

• Qubit oscillates like an L-C circuit

• Adjust potential to get two state system – “0” & “1”

• Want very low damping of oscillator

• High Q gives long lifetimes

Quantum behavior - potential that phase qubit lives in• Increase bias => cubic potential lifts degeneracy

231201 EEE • Use the |0> and |1> states for information

1 of lifetimeT1

T1’s in phase qubits – historically been short

13 m2 junctions: T1 ~ 25 ns

70 m2 junctions: T1 ~ 40 to 100 ns

0.5

0.25

00 100 200

T1 = 23 ns

Pro

b. |1

> s

tate

Meas. delay (ns)

• Loss mostly external to junction

Coherence of first phase quantum bit

0

1

• Single operation time can be ~ 1 ns

• Information in system decayed rapidly ~ 100 ns

• Need to preserve information > 104 x operation time to be useful

• => Increase coherence times & measurement fidelity!

Materials development – can we improve coherence?

• Absorption in dielectric & junction (a-SiO2) & (a-AlO2)• Gets worse at low temperature (two – level fluctuators)

Si

a-SiOx

Al

Focus on:• Insulators: along traces & around junction

in substrate

crossovers• Tunnel barrier - between superconductors

2 RSiO2Ceff 27ns

~T

RSiO2

=2.1k

Test actual L-C resonators using thin SiO2Q decreases at low temperature!

•TLS bath saturates at high E (power), decreasing loss

Schickfus and Hunklinger, 1975

Two-level systems in a-SiO2

E d

SiO2 - Bridge bond

UDAmorphous material has all barrier heights present

High E

Low ELow E

Problem - amorphous SiO2

Why short T1’s in phase Josephson qubits?

Dissipation: Idea - Nature:At low temperatures (& low powers)environment “freezes out”:

dissipation lowers

dissipation increases, by 10 – 1000!

Change the qubit design:

find better substrates

find better dielectric & minimize insulators in design

Common insulator/substrate materials

• SiO2

– Bridge bond, unstable

• Amorphous films have uncompensated O- , H, OH-

• Si3N4

– N has three bonds – more stable

• Amorphous films, still have uncompensated charges, H

• 20% H for low T films, ~ 2% H in high T films

• Al2O3

– Amorphous – high loss, similar to a-SiO2, has H, OH- in film

– Single crystal (sapphire) - Very low loss system

Minimize, optimize dielectric & substrate

Rabi oscillations > 600 ns !!

Sapphire substrate + SiN insulator:

Time (ns)

Maximum Dielectric SiO2

Minimum Dielectric SiO2

Minimum Dielectric SiNx

Minimum Dielectric SiNx (UCSB, high T)

Phys. Rev. Lett. 95, 210503 (2005)

Can couple 2 qubits

=> Do logical operations in ~ 100 ns – density matrix

J. Martinis

Superconductor - Aluminum

I

Tunnel junction a- AlOx-OH-

Found improvements due to optimized materials in insulators

=> Can we improve the tunnel barrier?

Qubit spectroscopy• Increase the bias voltage (tilt)• Frequency of |0> => |1> transition goes down

Resonances

Increasebias

Effects of resonances

• Quench Rabi Oscilations – strong coupling to qubit

Rabi oscillations

Spectroscopy

Number & splitting of Resonators13 um2 junction 70 um2 junction

• Smaller area – Fewer resonators, larger splitting (strong coupling)

• Larger area - More resonators, smaller splitting (weaker coupling)

Resonances are randomly distributed

Two level systems in junction

Amorphous AlO tunnel barrier

• Continuum of

metastable vacancies

• Changes on thermal cycling

•Resonators must be 2 level,

coherent with qubit!

I

What we need:

Crystalline barrier-Al2O3

Poly - Al

Poly- Al

Existing technology:

Amorphous tunnel barrier a –AlOx – OH-

No spurious resonatorsStable barrier

Amorphous Aluminum oxide barrierSpurious resonators in junctionsFluctuations in barrier

Silicon

amorphous SiO2

Low loss substrate

Design of tunnel junctions

SC bottom electrode

Top electrode

Q: Can we prepare crystalline Al2O3 on Al?

Binding energy of Al AES peak in oxide60

59

58

57

56

55

54

900800700600500400300Annealing Temp (K)

AE

S E

nerg

y of

Rea

cted

Al (

eV)

Al in sapphire Al203

Metallic aluminum

Aluminum Melts

68

10 Å AlOx on Al (300 K + anneal) 10 Å AlOx on Al (exposed at elevated temp.)

Anneal the natural oxides Oxidize at elevated temp.

A: No

Chose bottom superconducting electrode to stabilize crystalline Al2O3 tunnel barrier

Elements with high melting temperature

Elements with TC > 1K

Elements that lattice match sapphire (Al203)

Elements that form weaker bond with oxygen than Al

Elements that are not radioactive

Use Re for Al2O3 barrier

LEED, RHEED, AugerRe

Sputtering

LoadLock

STM/AFM

UHV surface science &growth system

Al

Oxy

gen

O2

Al2O3 growth: Al thermal deposition under O2 exposureon top of base epitaxial Re.

• 1.5 nm RMS roughness

• 1-2 atomic layer steps

• Screw dislocations on mesas

• Stranski-Krastanov growth

– Initial wetting of substrate

• Formation of 3-d islands

– Islands fill in gradually

0.5 x 0.5 m100 nm Re Base layer @ 850 C on sapphire

Epi Re Grow Al2O3 @ RT+ Anneal @ 800 ◦C 4x10-6 Torr O2

3m

AFM/RHEED of single crystal Al2O3 on Re(0001)

Re(0001)

Al2O3

Source of residual two-level fluctuators:Al-Al2O3 interface?

Electron Energy Loss Spectroscopy (EELS) from TEM shows1. Sharp interface between Al2O3 and Re2. Noticeable oxygen diffusion into Al from Al2O3 ???

Distance (μm)O

xyge

n co

nten

t

Al2O3Oxygen is white Long tail Sharp

Oxygen Profile across the tunnel barrier

Al Re

Fabricate test junctions with epi-Al2O3 barrier

• Low sub-gap conductance

• First high quality junctions

made with epitaxial barrier

Re(0001)

Al2O3

Al

1/R vs. Areaat 300 K

V(mV)

I-V curve at 20 mKRe

Al

Epitaxial trilayer fabrication

• Change just one thing at a time

– Still have a-SiO2 insulator (max-insulator design)

– Polycrystalline Al on top of trilayer

Sapphire

epi-Re/Al2O3/Al

Al

Resonance data from epi-Re/Al2O3/Al junction

• Significantly reduced number & coupling of resonances

• All 3 of 3 qubits on chip showed same effect

• Rabi oscillations match with those expected for max-SiO2 design

5x Reduction of splitting density

• Residual splittings are interfacial effect

• ~1 in 5 oxygens at Al interface

• Agrees with reduced splitting density to 1/5

2 nm

epi-Re interface

non-epi Al interface

Oxygen0.43 nm

Outlook

• Integrating epi-Re into min-SiN devices

• Materials optimization is critical to solid state QC devices

• Investigating possibility of single crystal V-MgO barriers

– Opens the possibility of crystalline insulators

– Both V & MgO can deposit and crystallize at lower

temp.

• Other avenues

– Vacuum crossovers

– Minimize junction area using e-beam lithography

& shadow evaporation

Shameless optimism slide

• How many years in the future is too many?

BardeenBrattainShockley

Kilbey

50%

Quantum Information Logic – based on digital 0&1!

• Can only measure one direction at a time – U/D or L/R

• Quantum systems only remember 1 direction at a time

• Example – 4 way switch

Set in middle

• Quantum bit - “qubit”• up ≡1, down≡0 - left & right intermediate

50%

50%

Up/Down

Left/Right

50%Up

Down

Left

Right

MeasureVertical

MeasureHorizontal

Up

Down

Vertical

Prepare state & measure qubit

with pulse

Readout SQUID

w/o pulse

|0> |1> |1>|0> Check SQUID

t

Increase current bias to modify potential

Too much tilt

I ~ 1 - 20 A

Just right tilt

Experimental setup

• Qubit is operated at 20 mK

•

• Expected to reduce thermal

decoherence sources

Insert qubit pic here

Qubit L

Stripline (C-SiO2 )

Josephson Junction(L&C)

=> Measure “Q” of simple LC resonators at lot T

Qubit has SiO2 Cap in || with J.J. & around lines

SiO2 AlOx

Power dependence to parallelplate capacitor resonators

wave resonator

L

f [GHz]

Po

ut [m

W]

Pin lowering

Q of the resonator with SiO2

goes down as power decreases!

Parallel plate capacitor resonators w/SiO dielectric

C

L

=> Compare to capacitors with vacuum dielectric

=> With & without SiO2 over the capacitor

C/2 C/2

L

Dissipation is in SiO2dielectric of the capacitor!

~Pout

Interdigitated capacitor resonators

Power dependence of QLC for parallel plate capacitors

HUGE Dissipation

Q decreases with at very low power(where we run qubits)

Nphotons

QL

C

Explains small T1!

L

C

Strong coupling interaction of qubit with coherent resonator

qubit - |0> or |1>

res. - |g> or |e>

|0e>

|0g> 0

|1e>

|1g>

On resonance

E=0

Form either symmetric (+) or anti-symmetric (-) state

|1e>

|1g>E

Off resonance

Qubit-resonator coupled interaction

• On resonance, put qubit in |1>

• Wait some time, int/2

•Qubit goes into |0>

=>Wait int

Qubit goes back to |1>

with enhanced amplitude!

States oscillate

|1g> <=> |0e>

Resonator has longer

coherence time than qubit!

off

off

on

on

J. Martinis

Early history of Quantum Information

1982

“It seems that the laws of physics present no barrier to reducing the size of computers until bits are the size of atoms and quantum behavior holds sway.” Richard Feynman

Peter ShorFactoring Algorithm

1994

QC - Lov GroverQuantum Search

1996

1970’sQuantum CrypotographyStephen Weisner "Conjugate Coding“

David Deutsch”Quantum Computer”

1985

1991Entangled photons Artur Ekert

1984 Polarized photonsBennett, Brassard

Deutsch, Joszaalgorithm

“balanced function”1992

Resources - Quantum error correction• Classical – repetition code, need 3 bits: 0≡000, 1 ≡ 111

– Single bit flip:

• 001, 010, 100 => 0

• 110, 101, 011 => 1

• Quantum – Need to check two variables:

– Need 32 = 9 bits

1B0A

1110001110001110000

1110001110001110001

bit sign

• 1 “logical” qubit = 9 physical qubits

• Need hardware with high stability!

System of two qubits

BA

2 Qubits => 4 amplitudes

n Qubits => 2n

11d10c01b00aBA

1

0

1

0

...

010..00c

001..00b

000..00a

2128 = 3.4 x 1038