High fidelity Josephson phase qubits winning the war (battle…) on decoherence

• “Quantum Integrated Circuit” – scalable

• Fidelity breakthrough: single-shot tomography

• Tunable qubit – easy to use

• Two qubit gates – new results

Collaboration with NIST – Boulder

UC Santa Barbara

John MartinisAndrew ClelandRobert McDermottMatthias Steffen(Ken Cooper)Eva WeigNadav Katz

PDGS

Markus AnsmannMatthew NeeleyRadek BialczakErik Lucero

The Josephson JunctionSC

SC

~1nm barrier

Silicon or sapphire substrate

SiNx insulatorAl top electrode

Al bottom electrode

AlOx tunnel barrier

Josephson junction

2 = i2e

1 = i1e

IJ = I0 sin

V = (0 / 2) .

“Josephson Phase”

= 1 - 2

Qubit: Nonlinear LC resonator

23

2/3

000 /1

24II

IU

C

4/1

0

2/1

0

0

122

III

p

I RCLJ

Lifetime of state |1>

0 50.7

0.8

0.9

1

pU

10

2132

pn

nE

E /

1

RC

Up

U()<V> = 0

<V> pulse(state measurement)

I0

= 0/2I0cos nonlinear inductor

I cos I 0j V ) (1/L J

0 sin I I

LJ

2

V 0

1: Tunable well (with I)2: Transitions non-degenerate3: Tunneling from top wells4: Lifetime from R

E0

E1

E2

0

1

2n

n+11000~

Superconducting QubitsPhase Flux Charge

Ce

I

E

E

C

J

2/

2/2

00

104 102 1

Area (m2): 10-100 0.1-1 0.01

Potential &wavefunction

EngineeringZJ=1/w10C 10 103 105

Yale, Saclay, NEC, Chalmers

Delft, BerkeleyUCSB, NIST,Maryland

Josephson-Junction Qubit

|0>

|1>

• State PreparationWait t > 1/ for decay to |0>

• Qubit logic with bias control

• State Measurement: U(I+Ipulse) Single shot – high fidelity

Apply ~3ns Gaussian Ipulse

I pulse (lower barrier)

I = Idc + Idc(t) + Iwc(t)cos10t + Iws(t)sin10tphase

pote

ntia

l

) 2/(

)2(

z

wsy

wcx

I

IH

Idc(t) dcIE /10

2/)2/( 2/110C

2/)2/( 2/110C

1.0

0.8

0.6

0.4

0.2

0.00.80.70.60.50.40.30.2

|0>|1>|2>

Ipulse

Pro

b. T

unne

l

96%

|0> : no tunnel

|1> : tunnel

The UCSB/NIST Qubit

1

01

Idc

Qubit

Flux bias

1 0

Iw

VSQ

SQUID

microwave drive

Qubit

Flux bias

SQUID

ExperimentalApparatus

V source

20dB 4K

20mK

300K

I-Q switch

Sequencer & Timer

waves

IsIVs

fiber optics rf filters

w filters

~10ppm noise

V source~10ppm noise

20dB

20dB

Z, measure

X, Y

Ip

Iw

Is

Itime

Reset Compute Meas. Readout

Ip

Iw

Vs

0 1

X Y

Z

Repeat 1000x prob. 0,1

10ns

3ns 20dB

Spectroscopy

Bias current I (au)

10/ U

saturate

Ip

Iw

meas.

Mic

row

ave

fre

que

ncy

(G

Hz)

10(I)

26

few TLS resonances

P1 = grayscale

Qubit Fidelity TestsRabi:

Ramsey:

Echo:

T1:

Pro

bab

ility

1 s

tate

Large Visibility! T1 = 110 ns, T ~ 85 ns

~90% visibility

State Tomography

|0 |1

|0+ |1 |0+ i|1

y

x

X,Y

P1state tomography

• Good agreement with QM• Peak position gives state ), amplitude gives coherence

DAC-Q (X)

DA

C-I

(Y

)

|0

|1

X

Y

|0+|1

|0+i|1

Standard State Tomography (I,X,Y)

time (ns)

P1

I,X,Y

I

XY

0

1

10 10 i

|0+|1

State Evolution from Partial Measurement

tomography & final measurestate

preparation

15 ns 10 ns

|0+|1

Needed tocorrect errors.

First solid-stateexperiment.

N

p 110f

2

10i

partial measure p

Prob. = p/2“State tunneled”

Prob. = 1-p/2

|0

Iw

Ip

p

t

Theory: A. Korotkov, UCR

Partial Measurement

|0+|1

|0

pm

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Partial measurement probability p

Pol

ar a

ngle

M

(ra

d)

0 0.2 0.4 0.6 0.8 1 1.2Measure pulse amplitude V

max(V)

Azi

mut

hal r

otat

ion M

(ra

d)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.4

0.6

0.8

1

Partial measurement probability p

Nor

mal

ized

vis

ibili

ty

-30

-10

-20

0

/4

/2

3/4

p=0.25

p=0.75

Decoherence and Materials Im

{}/

Re

{}

=

= 1

/Q

<V2>1/2 [V]

future a-

Dielectric loss in x-overs

Where’s theproblem?

TLS in tunnel barrier

Two Level States(TLS)

New design

Theory: Martin et alYu & UCSB group

xtal Al2O3

a-Al2O3

New Qubits

60 m

SiNx capacitor

I: Circuit II: Epitaxial Materials

(loss of SiNx limits T1)

Al2O3

(substrate)

Al2O3

Re

Al

LEED:

Bias current I

wav

e fr

eq.

(GH

z)

Spectroscopy: epi-Re/Al2O3 qubit

~30x fewer TLS defects!

(NIST)

Long T1 in Phase Qubits

tRabi (ns)

UCSB/NIST

T1 = 500 ns

Rabi

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350 400

t [ns]

P |

1>

P1

(p

roba

bili

ty)

tRabi (ns)

These results:Conventional design

(May 2005):

• High visibility more useful than long T1

• T1 will be longer with better C dielectric

Future ProspectsCoherence

T1 > 500 ns in progress, need to lengthen T

STOP USING BAD MATERIALS!

Single Qubit operations work well

Coupled qubit experiment in DR

Simultaneous state measurement demonstrated

Bell states generated

Violate Bell’s inequality soon

Tunable qubit : 4+ types of CNOT gates possible

Scale-up infrastructure (for phase qubits)

Very optimistic about 10+ qubit quantum computer

Dielectric Loss in CVD SiO2

6.02 6.03 6.04 6.05 6.06 6.0710

-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

Frequency [GHz]

Pou

t [m

W]

f [GHz]

Po

ut [m

W]

Im{

}/R

e{

} =

=

1/Q

Pin lowering

HUGE DissipationC

L

<V2>1/2 [V]

Pin Pout

T = 25 mK

Theory of Dielectric Loss

Im{

}/R

e{

} =

=

1/Q

<V2>1/2 [V]

Two-level (TLS) bath: saturates at high power, decreasing loss

high power

Amorphous SiO2

von Schickfus and Hunklinger, 1977

E

Bulk SiO2: OHCi

3103 i %1OH C

SiO2 (no OH)

SiO2 (100ppm OH)

Theory of Dielectric Loss

Im{

}/R

e{

} =

=

1/Q

<V2>1/2 [V]

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

high power

Amorphous SiO2

von Schickfus and Hunklinger, 1977

E

Bulk SiO2: OHCi

3103 i %1OH C

SiNx, 20x better dielectricWhy?

Junction Resonances = Dielectric Loss at the Nanoscale

20

10

00.01 0.1 1

10.5

10.0

qubit bias (a.u.) splitting size S' (GHz)

N/G

Hz

(0.0

1 G

Hz

< S

< S

')

wav

e fr

eque

ncy

(GH

z)

13 m2

70 m2

13 m2

S/h

70 m2

avg. 5 samples:

New theory (suggested by I. Martin et al):

e d 1.5 nm

Al

Al

AlOx

S

SSA

dEdS

Nd 2/12max

2 ])/(1[

theory

CeEd

S 2/2nm5.1

210max

d=0.13 nm (bond size of OH defect!)Explains sharp cutoff

Smax in good agreement with TLS dipole moment:Charge (not I0) fluctuators likely explanation of resonances

2-level states(TLS)

.

Junction Resonances: Coupling Number Nc

0

10

2max

2

0

1

)ns 10/1(

/

)6/(

2

2 max

A

E

AS

dSS

S

A

i

S

0

1

qubit junction resonances …

Nc >> 1, Fermi golden rule for decay of 1 state:

2

max

2/

2/0

m 90/

10

10

max

A

AS

dEdSS

AN

SE

SE

S

c

Number resonances coupled to qubit:S

g

e

Statistically avoid withNc << 1 (small area)

Same formula for i as bulk dielectric loss

Implies i = 1.6x10-3, AlOx similar to SiOx (~1% OH defects)

E10

State Decay vs. Junction Area Monte-Carlo QM simulation:(-pulse, delay, then measure)

1.0

0.5

0.0100500

time (ns)

pro

ba

bili

ty P

1

A=2500 um2 (Nc=5.3)

A=260 um2 (Nc=1.7)

State Decay vs. Junction Area Monte-Carlo QM simulation:(-pulse, delay, then measure)

1.0

0.5

0.0100500

time (ns)

pro

ba

bili

ty P

1

A=2500 m2 (Nc=5.3)

A=260 m2 (Nc=1.7)

A=18 m2 (Nc=0.45)

Nc2/2

Need Nc < 0.3 (A < 10 m2) to statistically avoid resonances~ ~

State Measurement and Junction Resonances

)exp(

])/(2/exp[

1

102

1

p

iii

t

dtdESP

0

1

qubit junction resonances …

Nc’ >> 1, Landau-Zener tunneling:

2

210'

m1.0

mGHz 36.0

/

A

AhENc

Number resonances swept through:

tp

Couple to more resonances

With tp ~ 10 ns, explains fidelity loss in measurement!(10 ns)-1