1

0

Fluctuatingenvironment

-during free evolution -during driven evolution

A -meter

0 0A 1 1A

01n

ACdrive

Decoherence of Josephson Qubits :

G. Ithier et al.: Decoherence in a quantum bit superconducting circuit, PRB 2005

The Quantronium

1µm

boxqp

trap

dc gatedc gateµw

readout junction

TowardsQND readout

DECOHERENCE DURING FREE EVOLUTION

dephasingZA X

qubitrelaxation

( )X td

noise

01( )tdw DEPHASING (t) dt'01( ')td wj = ò

1

2 1 / 2

Vg

ˆ cos cosˆ ˆ2

JC gH = ( -N ) - /2E EN

B

_e

Decoherence sources in the quantronium circuit

-1€€€€€2

0

1€€€€€2 0

1€€€€€2

1

0

5

10

15

20

-1€€€€€2

0

1€€€€€2

01(

GH

z)

Ng

01 g/ N = 0 01/ = 0

optimal pointNg=1/2 , =0

no dephasingno current

00.20.40.60.81

02

46

02.557.510

00.20.40.60.81

02

46

Ng

nA

0 ˆ 1I

Ng drive 0 ˆ 01N

minimum relaxation due to

U

ˆ ˆ ˆcos cos g2

C JH = E (N- ) -E /2N

Decoherence in the Quantronium

1

0

01 gN ,( ) environment_e

B

Relaxation

2

01

2

01

ˆ1( )

ˆ

1

)

0

0 1 (

Ng

22=

i

S

S

N1T

0 ˆ 1 0i if balanced junctions !

2

(t)(t) dt

dt(t1

)2

01

2012

d d

l

w

w

ljl

ld

=

+

¶¶

¶¶

ò

ò

Pure dephasing010 1

i dte

P0

( 0)1

S T

( )T 1ie ejdj -=

not necessarily exponential

22t t

( )d2

S2

s 2exp[ ( )sinc ]nied

lj w

w w= - ò

Relaxation of the Quantronium

t

P0

T1=0.5µs

01mod s1

eN (1

T)

01 (GHz)

T1: 0.3-2 s

Free evolution coherence time T2 :Ramsey interferences

readoutFree evolution (rotation also)

01RF

0 Rabi

Rabi

/2 pulse /2 pulse

Projection Z

Ramsey interferences reveal decoherence of free evolution during the delay

ZA X

0.0 0.1 0.2 0.3 0.4 0.5 0.6

30

35

40

45

sw

itch

ing

pro

ba

bili

ty (

%)

time between pulses t (µs)

RF= 16409.50 MHz

0.0 0.1 0.2 0.3 0.4 0.5 0.6

30

35

40

45

sw

itch

ing

pro

ba

bili

ty (

%)

time between pulses t (µs)

Fit = 19.84 MHz

T = 500 +/- 50 ns

)..2sin(/ teTt

t

Characterizing dephasing: 1) decay of Ramsey fringes

best ones:

2 200 500T ns

typical sample

0 200 400 6000.2

0.4

0.6

T2 ~ 300 ns

= 0N

g = 1/2

delay t between /2 pulses (ns)

sw

itch

ing

pro

bab

ilit

y p

Fit with the linked cluster expansion: static approximation for noise during each pulse sequence( Makhlin Shnirman, Paladino, Falci)

Comparing envelope fits

“static” approximation( Makhlin Shnirman, Paladino, Falci)

gaussian noise

500 ns

Simple exponential

0 100 200 300

0.2

0.4

-0.141

Ng = 1/2

0.4

0.6

-0.023

0.2

0.4

-0.079

0.2

0.4

-0.099

0.4

0.6

0.504

0.4

0.6

0.512

0.4

0.6

0.520

0 100 200 300

0.4

0.6

0.528

Ng=1/2

-1€€€€€2

0

1€€€€€2 0

1€€€€€2

1

0

5

10

15

20

-1€€€€€2

0

1€€€€€2

Ng

=0

Delay between /2 pulses (ns) Delay between /2 pulses (ns)

Coherence away from optimal point

Ng=

P0 : Ng=1/2 =0

Ramsey oscillations

time

0.4

0.6

100 ns

best coherence at optimal point

100 200 300

40

45

T2, ~ 60 ns

t1=270 ns

time t2 (ns)

0 100 200 300 400 50020

30

40

50

T2 ~ 200 ns

/2=6.3%

time t1 (ns)

sw

itchi

ng p

roba

bilit

y (%

)

Characterizing dephasing: 2) phase detuning pulses

/2X /2Xt1

/2X /2X

t2

At optimal point

35

40

45

50

T2 = 50 ns

Ng = 3.4% x (2e)

sw

itch

ing

pro

ba

bili

ty (

%)

T2 = 43 ns

Ng = 4.0% x (2e)

20 40 60 80 100 120

35

40

45

50

T2 = 40 ns

Ng = 4.5% x (2e)

detuning pulse duration (ns)

20 40 60 80 100 120

T2 = 28 ns

Ng = 5.7% x (2e)

Characterizing dephasing: 2) charge detuning pulses

/2X /2X

-0.3 -0.2 -0.1 0.0

Ng = 1/2

/ 2

10

12

14

16

20 25

switching prob (%)

Fre

qu

en

cy (

GH

z)

0.5 0.4

f / f0 = 0

Ng

16.3

16.4

16.5

16.6

16.7

16.820 25 30 35

switching prob (%)

F

req

ue

ncy

(G

Hz)

Characterizing decoherence: 3) resonance linewidth

0 200 400 600 800 1000

30

40

50

60

Echo

Ramsey50.5MHz

switc

hing

pro

babi

lity

(%)

delay between /2 pulses (ns)

5) Probing the dynamics: spin echo experiments

/2 /20.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

-50

0

50

Mic

row

ave

ou

tpu

t vo

ltag

e (

mV

)

time (ns)

0 200 400 600 800 1000

30

40

50

60

Echo

Ramsey50.5MHz

switc

hing

pro

babi

lity

(%)

delay between /2 pulses (ns)

0 500 1000 1500

30

40

50

60

TEcho

~ 500 +/- 50 ns

T2 ~ 220 +/- 50 ns

switc

hing

pro

babi

lity

(%)

time between /2 pulses (ns)

0 500 1000

30

40

50

Direct mapping of echo amplitude

/2 /2

/2 /2

/2 /2

2ET T low frequency noise

0 500 10000.20.30.40.5

0 100 200 3000.20.30.4

0 50 1000.2

0.3

0 50 1000.2

0.3

0 500 1000 1500

0.3

0.4

0 500 1000 1500

0.3

0.4

0 500 1000 1500

0.3

0.4

0 500 1000 1500

0.3

0.4

0 500 1000 1500

0.3

0.4

Ng = 1/2

/ 2 = 0.023

sw

itch

ing

pro

bab

ility

p

0.079

0.164

0.248

delay t between /2 pulses (ns)

0.484

0.452

Ng = 0.500

= 0

0.435

0.419

Echo decay away from optimal point

-0.3 -0.2 -0.1 0.0

10

100

500

Coh

eren

ce t

imes

(ns

)

|/2|0.05 0.10

10

100

500Free decaySpin echo

|Ng-1/2|

Gaussian model

S

1/

4MHz

SNg

1/

0.5MHz

Comparison exp vs model noise spectral densities

Closer look at charge and phase spectral densities:

10-3 10-2 10-1 100 101 102 103 104 105 106 107

10-3 10-2 10-1 100 101 102 103 104 105 106 1071x10-8

1x10-7

1x10-6

1x10-5

1x10-4

1x10-3

1x10-2

1x10-1

1x100

1x101

1x102

1x103

1x104

[S(

)]

[] (Hz)

Ng

1/f 1/f

[] (Hz)

Phase noise Charge noise

Cut-off at .5 MHz !!

Vg

Ng

Partlyexternal

Decoherence in phase Qubits (at UCSB)

Increasing I (arb. Units)

(GH

z)

p1=0 :blue

p1=1 : red10

21

If

Level-crossings with two level systems

Martinis et al (2003)

spectroscopy

(GHz)

p1

Coupling to other degrees of freedom

2 level systems couple to qubit!

Oxyde? Tunnel junction? Relation to charge noise?

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

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

T1 still short : 100-150 ns

New Qubit design

60 m

SiNx capacitor

(loss of SiNx limits T1)

P1

(p

roba

bili

ty)

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

>

tRabi (ns)

Rabi oscillations

New junction technology ?II: Epitaxial Materials

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)

DECOHERENCE IN FLUX QUBITS

At NEC

Relaxation: T1 measurement

80

70

60

50

Sw

itch

ing

prob

abil

ity

(%)

1.61.20.80.40.0Time (s)

initialization to ground state is always better than 90% relaxation dominant classical noise is not important at qubit frequency

~ 4ns

delay readout pulse

T1 vs f~ 4ns

delay readout pulse

??

1 vs E: Comparison of two samplessample3 sample5

Random high-frequency peaks. Broad low-frequency structure and high-frequency floor.

Dephasing: T2Ramsey, T2echo measurement (sample5)

~ 4ns

t/2

readout pulse

~2ns

t/2

~2ns

t

correspond to detuning

readout pulse

Ramsey interference

spin echo

T2 vs f, vs Ib (sample5)f=f*Ib=Ib*

Notice: fitted with exponential decay

Exp+Gauss Exp

Ramsey

Extract flux noise

1

0

Fluctuatingenvironment

-during free evolution-during driven evolution-at readout

A -meter

0 0A 1 1A

01n

The Quantronium

1µm

boxqptrap

dcgatedcgateµw

readout junction

ACdrive

Decoherence of a qubit:

1

12 2

Bloch-Redfield description

11 0( )

( 0)

z

S

SFree

Decoherence: driven evolution versus free evolution

Driven at Rabi

2*

2

2

123 cos sin

cos4 2

( ) z RabiS

1*1

2 21 cos sin

2 2

0 500 1000 1500

30

35

40

45

50

55

Ramsey 7MHz T2 ~ 250 ns

/2X - Lock

Y 24 MHz - 3/2

X T*

1 ~ 600 ns

/2X - Lock

Y 24 MHz - /2

X T*

1 ~ 600 ns

switc

hing

pro

babi

lity

(%)

delay between /2 pulses (ns)

: Spin locking

/2X /2X

/2X /2XaY

1*1 2

Determination of T*1

*1 1T T

15 MHz

0.2

0.3

0.4

0.5

0.6 7.8 MHz

sw

itch

ing

pro

bab

ilit

y p

61 MHz

0 500 1000

0.2

0.3

0.4

0.5

0.6

4.0 MHz

30 MHz

pulse length (ns)0 500 1000

0.2

0.3

0.4

0.5

0.6 R0

= 2.2 MHz

Decay of Rabi oscillations with Rabi frequency

Determination of T*2 :

1 10 100

0

200

400

600

800

1000

T* 2

(ns)

Rabi frequency (MHz)

T*2 ~ 480 ns

Decay of Rabi oscillations with frequency

2*

2

2

123 cos sin

cos4 2

T (1-100MHz) 1µs

0 20 400

200

400

600

800

1000

Rabi 0

= 15.4 MHz

T* 2

(ns)

(MHz)

2T

*2 2T T

decoherence in the rotating frame ?

0 1 Z

1

0

X

Y

lab frame:

0 200 400 600 800

25

30

35

40

45

50

55

T = 300 + /- 30 nsdetuning=50M H zsw

itc

hin

g p

rob

ab

ility

(%

)

D e lay betw een /2 pulses (ns)

T2=300ns

Ramsey decay:

rotating frame:Z

I1*>

I0*>drive

* *0 1

T2*=480 ns

0 200 400 600 800 1000 12000.2

0.3

0.4

0.5

0.6

swit

chin

g p

rob

abili

ty p

pulse length (ns)

Conclusion: more robust qubit encoding in the rotating frame, but limited use.

NIST ChalmersNEC

TU Delft

CONCLUSIONS:

Framework for understanding decoherence

large decoherence:Coherence times up to 500 nsMicroscopic decoherence sources ??

Decoherence can be fought

QND readout achievable

quantum computing applicationspresently beyond reach

0.0 0.1 0.2 0.3 0.4 0.5 0.6

30

35

40

45

switc

hing

pro

babi

lity

(%)

time between pulses t (µs)

-1€€€€€2

0

1€€€€€2 0

1€€€€€2

1

0

5

10

15

20

-1€€€€€2

0

1€€€€€2

The work on

YALE

SPECELECTQUANRONICSUM

GROUP

I. SIDDIQIF. PIERREE. BOAKNINL. FRUNZIO

R. VIJAYC. RIGETTIM. METCALFEM. DEVORET

G. ITHIERE. COLLINN. BOULANTD. VION P. ORFILA P. SENATP. JOYEZP. MEESOND. ESTEVE

Karlsruhe

Landau

Roma

A. SHNIRMANG. SCHOENY. MAKHLINF. CHIARELLO

1

0

Fluctuatingenvironment

A -meter

0 0A 1 1A

01n

the Quantronium

1µm

boxqp

trap

dc gatedc gateµw

readout junction

Appl. Physics

SQUBIT

Thanks toNEC / Japan

2004

ELECTQUANRONICSUM

GROUP

Towards QND readout ‘at’ optimal point

flux qubit : charge qubit :

SQUID inductance quantum capacitance

Chalmers, Helsinki

charge-phase qubit :

readout junction inductance

Quantum capacitance

C/C

J

0

1

TU Delft Yale, Saclay

0

1

PULSE IN

PULSE OUT

U

“RF” pulse

dynamics in anharmonic potential

more complex, but:

-better fidelity ?-no reset: possibly QND

switching

dc pulse

simple, but:

-fidelity 40%-qubit reset : NOT QND

t

U

rf readout (M. Devoret, Yale)

dc versus ac readout in the quantronium

M. Devoret team at Yale I. Siddiqi et al., (2004)

µW Pulse IN

QuBitcontrol

0 1

0

1

OUT

-1€€€€€2

0

1€€€€€2 0

1€€€€€2

1

0

5

10

15

20

-1€€€€€2

0

1€€€€€2

Towards non destructive readout at optimal point with an AC drive

UJop

timal

P

1

001n

Similar dispersive methods developed for other qubits

M. Devoret team at Yale I. Siddiqi et al., (2004)

µW Pulse IN

QuBitcontrol

0 1

0

1

OUT

UJop

timal

P

1

001n 01

180°

-180°

am

plitu

de

µW drive amplitude

µW

pha

se

State dependent bifurcation

The Josephson Bifurcation Amplifier

Enhanced

300 K

Quantronium from Yale

Quantronium + JBA SETUP

4 K

0.6 K

30 mK

1.3-2GHz

MS

-20dB

-30dB0 100 200 300 400

0

1

2

3

4

VM (

V)

time (ns)

Q

50

TN=2.5KG=40dB

G=40dB

ILO

demodulator

bifurcation

NO bifurcation

-6.8 -6.6 -6.4 -6.20.0

0.2

0.4

0.6

0.8

1.0

Bifu

rca

tio

n p

rob

ab

ility

readout µW input power (dB)

0 20 40 60 80 100 120 140 160

gate µW pulse duration (ns)

45-5

0%

Rabi oscillations with the JBA

Contrast : 50%

0

1

100ns 125ns

JBA pulse

(Saclay exprt)

1 0

100ns 125ns5n

s

20ns

40ns

JBA readout

10ns

gate

100ns

0

1

0

1

0

1

0

1

partially QND

initial finP( , , ral esult)

1

0 0

10

34%

100%

66%

0%

10

25%9%

30%36%

1

10

17%83%

10

0%0%

Notice: relaxation againpartly avoidableby tuning the qubit

0

1

Quantum Non Demolition ? read twice

initial A B

& correlations

Note: results for flux-qubit now available

Dispersive readout of the flux qubit

detection

Tdetection

Tplateau

switching

time

Iac

A. Lupascu et al.TU DELFT

Activation rates for different detuning values

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.0

0.5

1.0

1.5

2.0

2.5

3.0

Tplateau

=400 ns

Tplateau

=80 ns

I ac

2 (au

)

ln(a/)2/3

F = 775 MHzFres=822 MHz

Tk

U

attsw

Be

2

2

0 1B

acaa I

I

2/32

1

B

acdyn I

IuU

2033

4 pa RC

Iac,bifurcation2

slope=udyn/(kT)

Thy: M. Dykman

Rabi oscillations with optimal settings

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

Psw

Dt (ns)0 10 20 30 40 50 60 70 80

0

2

4

6

8

10

12

14

Psw

Dt (ns)

0.1 1

0.01

0.1

FR

abi (

GH

z)

Imw

(au)

Dt = length of MW pulse

Ramsey oscillations with optimal settings

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0

97 %

Psw

Dt (ns)

11 %

Rabi oscillation

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.0

Psw

tRamsey

(ns)

Ramsey: ge-mw= 69 MHz

Ramsey frequency vs detuning

4.50 4.55 4.60 4.650

10

20

30

40

50

60

70

80 F

Ramsey

|Fmw

-Fqubit

|

FR

amse

y (

MH

z)

Fmw

(GHz)

Relatively strong low frequency fluctuations visible in the drift of the Ramsey frequency.

QND data : analysis in progress

A Circuit Analog for Cavity QED2g = vacuum Rabi freq.

= cavity decay rate

= “transverse” decay rate

L = ~ 2.5 cm

Cooper-pair box “atom”10 m10 GHz in

out

transmissionline “cavity”

Blais, Huang, Wallraff, Girvin & RS, cond-mat/0402216; to appear in PRA

Cavity QED with a Cooper pair box: first dispersive readout

R. Schoelkopf, A. Wallraff, S. Girvin et al., Yale (2004)

Dispersive readout with out of resonance photons

Dressed Artificial Atom: Resonant Case

? T01 R

2g

/ R

T

2

1“vacuum Rabi splitting”

Rabi Oscillations of Qubit

Prf = 0 dB Prf = +6 dB

Prf = 18 dB

Coherence time measurementswith 2 pulse Ramsey sequence