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Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed

Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Semiconductor qubits for adiabatic quantum computing

Malcolm Carroll

Sandia National Labs, Albuquerque

June 11th, 2014

Spin read-out & Rabi oscillations Silicon P donor qubit structure

~10 P

P

Local ESR

Adiabatic inversion

Ramp time [us]

DQD qubits for QA

• Motivation for Si qubit research in adiabatic QC and QA

• Single electron spin qubit and adiabatic operation

• Semiconductor qubit approaches to quantum annealing

• Summary

Outline

2

What are the limits and extensions of adiabatic control of one or several qubits? (e.g., adiabatic inversion)

Questions about quantum annealing

• Are there tests with one and a few qubits that inform the “black box” testing approach

• What are the microscopic dynamics and how does it break?

o Is fast relaxation helpful? (what dependence?)

o kT >> Egap ?

o What role does T2 play?

• What makes a good qubit for quantum annealing?

o Is there benefit to using a semiconductor qubit for QA?

Our approach:

• Examine silicon (or semiconductor) qubits in context of adiabatic quantum computation (or annealing)

Motivations and research direction

?

4




• Summary

Outline

5

Kane-like (electron spin only):

Single donor for qubit

One electrode on/off – frequency tuning to NMR or ESR u-waves

Second electrode on/off – overlap electrons for exchange (sqrt[SWAP])

Lot’s of progress in this area recently

Not clear how people will couple donors but focus of this talk is context of adiabatic control for single spin

Qubit approach using donors in Si

Kane, Nature, 1998

6

Concept

SET or QD detects nearby charge center ionization

Spin dependent ionization

Single donor spin read-out concept

7 Morello et al., Nature 2010

Charge state is static

Charge state is changing in time due to tunneling

2. Read

1. Load

3. Unload

Read sequence (spin up)

SET donor EC

Poly silicon quantum dot

1.2V 0 V

0 V 0 V

Si

SiO2

current

Poly-Si

• Simplify SET for donor read-out o Implant will be self-aligned

Harvey-Collard

500 nm

LP RP

8

S/D

E=𝑞

𝐶

Single dot

Poly silicon quantum dot

1.2V 0 V

0 V 0 V

Si

SiO2

current

Poly-Si

• Simplify SET for donor read-out o Implant will be self-aligned

• Relatively regular period Coulomb blockade achieved in poly silicon SET

• Wire width ~50-60 nm with gaps between wire and plunger of ~40-50 nm

• This structure can regularly be used for read-out

Harvey-Collard

500 nm

LP RP

9

S/D

E=𝑞

𝐶

Single dot

QCAD is semi-classical simulation capability developed at SNL

1.1x1017/cm3 charge fits 4K threshold

Order of ~5x1010/cm2

Gate to quantum dot capacitances are similar to QCAD predictions in multiple devices

Semi-classical modelling of lithographic dot

Shirkhorshidian

Dot location

10

Typical implant conditions:

120 keV implant, range ~28 nm below SiO2/Si interface, 18 nm vertical straggle

4e11/cm-2 dose → ~ 14 Sb donors in 60 x 60 nm2 window

Charge offsets are seen in these implanted poly-MOS devices

Gate wire with implant – QD coupling to donor

Si

SiO2

Poly-Si

Sb

T ~ 2K

11

Implant window

Tuning spin readout

12

Spin bump with 256 averages

Measure Unload Load

Ez

Reservoir

Donor

Ez Reservoir

Ez Reservoir

Load

Read

Unload

Lilly

up

All down would have no “bump”

ESR pulse sequence – two level pulse

13

1. At the end of the readout pulse, a spin down is loaded. (b) 2. Pulse energy levels down to manipulate. (a) 3. Apply microwaves. (a) 4. Spin readout (b)

Donor

Ez

Reservoir Donor

Ez Reservoir

(a) plunge and ESR (b) read

Electron spin resonance of single spin

14

o Two level test with ESR detects spin resonance o Phosphorus implanted sample (~ 400 nm from center) o Similar approach to Al-Si SET devices [Pla et al. (2012)]

Nguyen

B=1.3T P = 0 dBm

Read/initialize level Hold/u-waves

Time [ms]

14

Resonance frequency drifts

15

These two scans were taken 10 min apart.

p

Electron spin

Nuclear spin bath

o 29Si can reorient over timescales of ~sec, and the electron resonance frequency shifts due to hyperfine coupling.

o ~5-10 MHz line width or equivalent of ~ 0.2-0.3 mT o Bac max ~0.1 mT

Lilly

Incomplete pulsed X rotations due to spin bath diffusion

16

• 128 averages per trace • 150 repeats • Fixed frequency (36.459 GHz)

• For a fixed rotation (~pi pulse)

time: • sometimes the spin signal

is small, sometimes large

Lilly

Microwave field dependence

17

z

x’

Bx

z

x’

Bx

0 dBm 3 dBm 6 dBm

frabi= 1.4 MHz frabi= 2.8 MHz frabi= 2.1 MHz

Lilly

Magnetization follows a complicated track

Constant precession around Z-axis can be separated out in rotating frame

ESR pulse for X rotation is notionally a diabatic pulse when on resonance

Adiabatic inversion starts off resonantly and transitions slowly through resonance (LUBO)

Rotating frame

Adiabatic inversion (pi rotation)

i

k

18

Adiabatic sweep compared to on-resonant pulse

Spin

bu

mp

sig

nal

Pulsed pi rotation “on resonance” Adiabatic Sweep Hold Read Read Hold

Luhman

Df/t<<frabi

2

Df=25 MHz; t=10 us

Adiabatic approach

19

p

Electron spin

Nuclear spin bath

Characterization of adiabaticity of sweep

-5 dBm 0 dBm

Luhman 20




• Summary

Outline

21

List of metrics for QUBO example Physics of encoding

• Z, ZZ, X interactions & low measurement error (also independent control) • Tqubit loss

Metric: Max. time of computation because no error correction for leakage in quantum annealing

• Large (Egap)2 / tcomputation-time Measure: computation time limit before excitation error due to Landau-Zener tunneling This will be a prefactor in the scaling as gap of problem shrinks exponentially Excited state manifold of single qubit should also be well separated

• Texcite/ (Egap)2 at Egap ~O(kT) Measure: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kT > gap) Also details of the specific qubit interaction with its open system could be important in scaling

How important is cascade of low weight Hamming error to larger Hamming error? What Hamming distance are the bath interactions for each qubit instance?

• Correlation length (?) Need a metric for coupling between high weight Hamming transitions Notionally, large domains “coherently tunneling” to find energetic minima (non-classical hopping)

Engineering of encoding • Parameter-tuning-range/noise • High yield (uniformity – variance in parameters) or accurate characterization • Scalability (integration, routing, power)

What makes a good quantum annealing qubit?

22


• Z, ZZ, X interactions & low measurement error (also independent control)

23


Single spin encoding

1

0

BZ

BX

Tt )0(

)0()( 2121212211 tHSSSSSSJSBSBH inityyxxzzzzzz

1. Difficult to tune local B-field for each spin

2. Exchange is not a true ZZ term

Two spin Hamiltonian

)(2121 tHmlkH initzzzz

| R > | L >

En

ergy

| L > | R >

Charge qubit encoding for QUBO

24

Modulation of k and l can be accomplished with voltages on gates

Negative and positive epsilon might range from -meV to +meV [~12-13 K]

Can be several orders of magnitude greater than the temperature in the dot

V

VH

0

02,1

Voltage


Initialization

Tunneling magnitude is independently tunable from possibly less than neV to 100 ueV (likely greater)

Only positive

0

02,1 t

tH

''

0 RL

| R > | L >

En

ergy

| L > | R >

2 t

25


Coulomb interaction for qubit coupling 26

Interaction magnitude experimentally found to range from 25-85 ueV [~0.25-1K]

Strength of Z1Z2 interaction tunable (by construction or FET couplers) & might be made larger

A little tricky to build pure ZZ but can minimize cross terms

H-litho using donors is possible path that might address both achieving high fidelity & biger ZZ

Van Weperen, PRL, 2011

L. Trifunovic et al., arXiv 1110.1342

26 Bussmann

27

Other interactions for charge qubit

Available interactions

• Z interaction • X interaction

ZZ interaction −ZZ interaction XX interaction XZ interaction

Speculative interactions

XZ Donors: Superior alignment? Previously proposed by Hollenberg et al.

27 Landahl, Jacobson


Two spin approach

Motivation: • Try to leverage benefits of spin as qubit encoding (low effective kT near E-min-gaps) • k,l range is defined by magnitude of J for each DQD • 2-qubit coupling is similar approach as charge qubit

Challenge: • Possible problem with meta-stability (bigger problem for AMO approaches?) • S/T- also possible • Weak initialization fields for both? This sets max E of parameters (speed/size of computation limit?)

02,1

Z

Z

dB

dBJH

poly

B

Inductor? Bz,1 Bz,2

Qubit sub-space

| ↓↓ >

| ↑↑ > | ↑↓ > + | ↓↑ >

| ↑↓ > - | ↓↑ > En

ergy

V

J

28

• Motivation for research in adiabatic QC and QA



• Summary

Outline

29




• Large (Egap)2 / tcomputation-time Measures: computation time limit before excitation error due to Landau-Zener tunneling Excited state manifold of single qubit should also be well separated

• T1/ (Egap)2 at Egap ~O(kT) Measures: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kT > gap)


30

?




• Large (Egap)2 / tcomputation-time Measures: computation time limit before excitation error due to Landau-Zener tunneling Excited state manifold of single qubit should also be well separated

• T1/ (Egap)2 at Egap ~O(kT) Measures: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kT > gap)


31

? Start with Si charge qubit as test platform

Charge qubit encoding for QUBO (example)

32

Charge qubit is based on two level approximation of DQD Encoding is left / right Gap is dependent on tunnel coupling between wells Detuning established with lateral electric field

e

|L> |R>

Nordberg et al., PRB 2009

Characterization of energy dependent relaxation

Developed measurement technique and analysis to extract relaxation time and dependence on energy

Related to work done by Harbusch et al. PRB 2010

Non-adiabatic (fast ramp)

Adiabatic (slow ramp)

34

?

Square pulse (f & r)

tmeasure

tramp

215 Hz 860 Hz

8600 Hz 3010 Hz

• Super-Ohmic model leads to peaks growing closer together with frequency • Ohmic spectral leads to different qualitative signature of peak merging • Super-ohmic fits experiment better – good fit with acoustic phonons

Illustrative model

Jacobson

35

arXiv:1403.3704

QIST contributors at SNL Qubit fab: M. Busse, J. Dominguez, T. Pluym, B. Silva, G. Ten Eyck, J. Wendt, S. Wolfley Qubit control & measurement: N. Bishop, S. Carr, M. Curry, S. Eley, T. England, M.

Lilly, T.-M. Lu, D. Luhman, K. Nguyen, M. Rudolph, P. Sharma, A. Shirkhorshidian, M. Singh, L. Tracy, M. Wanke

Advanced fabrication (two qubit): E. Bielejec, E. Bussmann, E. Garratt, A. MacDonald, E. Langlois, B. McWatters, S. Miller, S. Misra, D. Perry, D. Scrymgeour, D. Serkland, G. Subramanian, E. Yitamben

Device modeling: J. Gamble, T. Jacobson, R. Muller, E. Nielsen, I. Montano, W. Witzel, R. Young

Joint research efforts:

o Australian Centre for Quantum Computing and Communication Technology (D. Jamieson, A. Dzurak, A. Morello, M. Simmons, L. Hollenberg)

o Princeton University (S. Lyon) o NIST (N. Zimmerman) o U. Maryland (S. Das Sarma) o National Research Council (A. Sachrajda) o U. Sherbrooke (M. Pioro-Ladriere) o Purdue University (G. Klimeck & R. Rahman) o U. New Mexico (I. Deutsch, P. Zarkesh-Ha) o U. Wisconsin (M. Eriksson) o University College London (J. Morton, S. Simmons)

QIST team & external connections

36

Summary

37

o Silicon electron spin qubit is platform for ESR experiments (limits of adiabatic control?) • Fairly well understood noise

o Adiabatic control scheme improves spin inversion probability • This is the same control as LUBO • Background nuclear spins in natural silicon produce diffusion of resonant frequency

o Discussed different encodings of semiconductor qubits for quantum annealing • DQD could work (charge or spin) • Possible advantages in min-gap energy, fab precision (i.e., accurate Hamiltonian) &

perhaps relaxation dynamics • Two pulse scheme identified as general way to characterize spectral density of

relaxation processes • Si MOS charge qubit spontaneous emission consistent with acoustic phonons

Spin read-out & Rabi oscillations Silicon P donor qubit structure

~10 P

P

Local ESR

Adiabatic inversion

Ramp time [us]

DQD qubits for QA

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