readout of superconducting flux qubits

Readout of superconducting flux qubits

Hideaki Takayanagi 髙柳英明NTT Basic Research Laboratories

H. Tanaka, S. Saito, H. Nakano, H. Tanaka, S. Saito, H. Nakano, J. Johansson, F. Deppe, J. Johansson, F. Deppe, T.Kutsuzawa,and K. SembaT.Kutsuzawa,and K. Semba NTT Basic Research Labs. Tokyo University of Science CREST JSTM. UedaM. Ueda Tokyo Institute of TechnologyM. ThorwartM. Thorwart Heinrich Heine UniversityD. HavilandD. Haviland KTH

Posters : Nakano (Berry Phase) Johansson （ Vacuum Rabi)

Frontiers in Quantum NanoscienceA Sir Mark Oliphant & PITP ConferenceNoosa Blue Resort, 24 January 2006

Sample size Sample size ～～ μm μm

Loop sizeLoop size SQUIDSQUID ~ 7 ~ 7 x 7 x 7 mm22

qubitqubit ~ ~ 5 x 55 x 5 mm22

Mutual inductance Mutual inductance MM ~ 7 pH ~ 7 pH

Josephson junctionsJosephson junctionsAl / AlAl / Al22OO3 3 / Al/ Al

Junction areaJunction areaSQUIDSQUID : : 0.1 x 0.0.1 x 0.0808 mm22

qubitqubit : 0.1 x 0.2 : 0.1 x 0.2 mm22, , ( ( = 0.7 ) = 0.7 )

• e-beam lithographye-beam lithography• Shadow evaporationShadow evaporation• Lift-offLift-off

Oxide layer

Aluminum layer

PMGI

ZEP

Silicon

SiO2J osephson junction

Oxide layer

Aluminum layer

Oxide layer

Aluminum layer

PMGI

ZEP

Silicon


PMGI

ZEP

Silicon

SiO2

ZEP

Silicon

SiO2

Silicon


J osephson junction

5 m

IC(SQUID)~ 0.5 A

IC(qubit)~ 0.7 A

M Iq ISQ ~ 3.7 GHz

Multi-photon transition betweenMulti-photon transition between superposition of macroscopic quantum states superposition of macroscopic quantum states

E 0

(1)

1.5101.5051.5001.4951.490

qubit

/

h

< I

P >

T

1.5101.5051.5001.4951.490

qubit

/

1 1

1

12

3

32

233

2

2h

＋

ｰ

( ) /√2 　 ground state

( ) /√2 　 1st excited state

Multi-photon transition

Macroscopic Quantum state Transition induced by energy difference of single photon.Macroscopic Quantum state Transition induced by energy difference of single photon.Any superposition state can be prepared by adjusting a duration of resonant MW-pulse.Any superposition state can be prepared by adjusting a duration of resonant MW-pulse.

extext : magnetic flux : magnetic flux

Resonant Resonant microwave photonmicrowave photon

Superconducting Superconducting persistent current persistent current ~ 0.5 ~ 0.5 AA

( ~ 10( ~ 1066 cooper pairs ) cooper pairs )

QubitGround state

Qubit Excited state

Analogy of Schroedinger’s catAnalogy of Schroedinger’s cat

superposition of macroscopically distinct statessuperposition of macroscopically distinct states

Multi-photon spectroscopyMulti-photon spectroscopy

SQUID readout

-2

-1

0

1

2

d I

SW (

nA

)

1.5041.5021.5001.4981.496

qubit /

0

RF : 3.8 GHz

-10 dBm

１

１2

23

2

1

0

-1

-2

d I

SW (

nA

)

1.5041.5021.5001.4981.496

qubit /

0

RF : 3.8 GHz

0 dBm

１

１ 2

2

3

=0.86GHz

1-photon

2 -photon

Multi-photon transition

S. Saito et al., PRL 93, 037001(2004)

31

Single color Multi photonSum frequency

Two colorsTwo photonsSum frequency

Two colorsTwo photonsDifference frequency

Multiphoton Rabi

1

2

1

2e

g

ee

g g

Observation of multiphoton Qubit control by microwave pulse.

Y. Nakamura, et al., PRL(2001)

measurement

Ibias

t

Vmeas

t

0

0

Vth

70 ns

400 V

tRF pulse

1200 ns

repetition: repetition: 3.3kHz ( 300 3.3kHz ( 300 s)s)

Non-switchingNon-switching

switchingswitching

Discrimination of the signal

RF pulse

~100 nA

|g>

|e>

tσ̂

x

y

z

|g>

|e>

|e>

|g>

Sw

itch

ing

pro

bab

ility

5040302010MW pulse length [ns]

6dBm3

-10

-14

-33

20 %

-22

-27

Sw

itch

ing

pro

bab

ility


12dBm8

3

-2

-10

20 %

-6

Sw

itch

ing

pro

bab

ility


2dBm

1

0

-1

-4

20 %

-2

Sw

itch

ing

pro

bab

ility


12dBm

10

86

2

20 %

4

Single color & Multi photon

e

g

1-photon Rabi 2-photon Rabi 3-photon Rabi 4-photon Rabi

10.25GHz x 310.25GHz x 3 rfRabi VaJ n[MHz] 17352

][mV 0134.0 -1anumberphoton : n

frequency Rabi : 2Rabi amplitude pulseMW : rfV

1200

800

400

0Rab

i fre

quen

cy [M

Hz]

300250200150100500

MW pulse amplitude [mV]

2

n = 1

34

Sw

itch

ing

pro

bab

ility


16.2GHz, 10dBm

6

2

-5

-10

20 %

Sw

itch

ing

pro

bab

ility


16.2GHz, 10dBm

6

2

-5

-10

20 %

Two colors, Two photons & Sum frequency

e

g

500

400

300

200

100

0

Rab

i fre

qu

ency

[M

Hz]

16012080400Vrf1 [mV]

04 6 10dBm

16.2GHz

6dBm

10.25GHz8dBm

2-5-10

4

2

0

-4

-7

-10

8

10.25GHz, - 4dBm 10.25GHz, 4dBm

10.25GHz

16.2GHz

Sw

itch

ing

pro

bab

ility


11.1GHz, 4dBm

2

10 %

0

-2

-5

-10

Sw

itch

ing

pro

bab

ility


11.1GHz, 4dBm

2

10 %

0

-2

-10

-5

Two colors, Two photons & Difference frequency

e

g

350

300

250

200

150

100

50

0

Rab

i fre

qu

ency

[M

Hz]

806040200Vrf1 [mV]

0

2

4dBm11.1GHz

18.5GHz, 8dBm

4

-10

2

-20

-5

18.5GHz, 0dBm 18.5GHz, 8dBm

11.1GHz

18.5GHz

Discussion

2

1

2

1 2

1

22 iii

iizxz aaaagH

ii

2

1

cos222 i

iizxz tgH

Assume that the microwave is in the coherent state as tia iii exp

tHtt

i

gtbetat

g

nm

tnmEi

nmnm

g nmE

e

E

gJ

E

gJ

EtbtP

, 212

21

1

2 1441

21

With the conditions21 E E

2

211

11Rabi

44

gJ

gJ

0

Ene

rgy

Lev

el

0.5020.5010.5000.4990.498

Eg

e

is the solution of

The probability to find the state in the ground state is

350

300

250

200

150

100

50

0R

abi f

req

uen

cy [

MH

z]806040200

Vrf1 [mV]

0

2

4dBm11.1GHz

18.5GHz, 8dBm

4

-10

2

-20

-5

Comparisions between experiments and calculations

500

400

300

200

100

0

Rab

i fre

qu

ency

[M

Hz]

16012080400Vrf1 [mV]

04 6 10dBm

16.2GHz

6

10.25GHz, 8dBm

2-5-10

4

2

0

-4

-7

-10

8

rf221rf111Rabi VaJVaJ

Sum freq. Difference freq.

a1 = 0.00741[mV-1]a2 = 0.0131

a1 = 0.0118 [mV-1]a2 = 0.00911

[MHz] 17352

Rabi Oscillation : Quantum bit oscillates between and with a frequency that is proportional to the amplitude of irradiated microwave.

0 1

pulse ： width of pulse

+

A

B

A’

B’

A B A’B’0 0 0 00 1 0 11 0 1 11 1 1 0

When A=1,B is reversed.

Controlled-not gate0

1

Rotation Gate

Control Gates

)1(102

12

sin02

cos ie Any multiple qubit logic gate may be composed

from CNOT and single qubit gates.

ＲａｂｉＲａｂｉ

56

54

52

50

48

46

Pro

babi

lity(

%)

100908070605040302010

Pulse Width (ns)

(t)0

1

by phase shiftby phase shift ※ ※ in a rotating framein a rotating frame

12

sin02

cos)(

iet by introduce detuningby introduce detuning

)(t

RamseyRamsey

Control ofControl of

π/2Pulse

π/2Pulse

Control of Control of

Control of two angles in Bloch sphere Control of two angles in Bloch sphere q q （（ RabiRabi ）） andand 　（　（ RamseyRamsey ））

longitude

latitude

1

0

　　 with detuningwith detuning

0

1

Phase shift without detuningPhase shift without detuning

π/2Pulse π/2Pulse

π/2Pulse π/2Pulse

Rapply ff

0

dfff Rapply ⊿ ｔ12

⊿ ｔ12

t

t

Ψ

Ψ

※ ※ in a rotating framein a rotating frame

Detuning method vs. Phase shift methodDetuning method vs. Phase shift method

Equator

]2mod[ 12tfR

Ramsey Ramsey （（ detuning method ddetuning method d ｆｆ ~0.2 GHz~0.2 GHz ））

π/2Pulse

⊿Φ ＝０

π/2Pulse

π/2Pulse

π/2Pulse

fR ： RF ~ 11.4 GHz

⊿Φ ＝ π

⊿Φ ＝ π/2

T=1/fR ～ 88ps

Ramsey Ramsey （（ phase shift method dphase shift method d ｆｆ =0 Hz=0 Hz ））

T=1/df ～ 5ns

Advantage of Phase shift methodAdvantage of Phase shift method

1SWP

]mod[ 12tR

URF

URF

Vext

｜１＞

｜０＞

Read out voltage

T=25mK

0

1π/2Pulse

⊿ ｔ12

π/2Pulse

ensemble ：１ 0,000

Ψ

Measurement schemeMeasurement scheme

３３ . Fast Oscillation. Fast Oscillation

Dephasing time1.84[ns]

Resonant Frequancy１１．４ [GHz]

Frequancy by fitting11.18±0.01 [GHz]

π/2 pulse => ５ [ns]

50

45

40

35

30

Psw

[%

]

2. 01. 81. 61. 41. 21. 0 t12 [ns]

Av ： 10,000 times

⊿Φ ＝０ ⊿Φ ＝ π⊿Φ ＝ π/2 ⊿Φ ＝ 3π/2

TPhaseShift=89 ps

• We succeeded in observing Larmor precession ( 11.4 GHz )We succeeded in observing Larmor precession ( 11.4 GHz ) of a flux qubit with phase shifted double pulse method.of a flux qubit with phase shifted double pulse method.　　　　 An arbitrary unitary transformation of a single qubit is possible.An arbitrary unitary transformation of a single qubit is possible.

　　

・・ AdvantageAdvantage

＞＞ We can control qubit phase rapidly ( ~ 10 GHz ).We can control qubit phase rapidly ( ~ 10 GHz ).　　　→　　　　→　 We can save time for each quantum-gate operationWe can save time for each quantum-gate operation　　　→　　　　→　 Compared with the detuning method (~ 0.1 GHz ), Compared with the detuning method (~ 0.1 GHz ), 10 10 ～～ 100 times many gates can be implemented.100 times many gates can be implemented.

Artificial Atom in a Cavity

Cavity QED

A. Wallraff et al, Nature 431, 162 (2004)I. Chiorescu et al, Nature 431, 159 (2004)

E/M shielding (-100 dB) &

Three-fold -metal shield

RF-line

Ibias -line

Vm-line

sample package

RF-line

Ibias-line

Vm-line

Dilution refridgerator

(~ 20 mK)

Measurement systemMeasurement system

Microwave line

Csh

I bias V meas

5 m

qubit

SQUID

V measI bias

MW

On-chip component 　[1] LC mode 、 filtering　　 capacitor( Csh ) resistor ( Ibias, Vmeas )[2] strong driving ：　　 microwave line

Sample

Csh

Microwave line

I bias V meas

Csh

LleadLlead

15

10

5

0

Res

onan

t fr

eque

ncy

[GH

z]

1.5101.5051.5001.4951.490

qubit /

0

EJ = 200 GHz

= 1.7 GHzfres = 4.3 GHz

Qubit Qubit coupled to a spatially separatedcoupled to a spatially separated LC-harmonic oscillator LC-harmonic oscillator

QubitQubit

Coherent dynamics of a flux qubit coupled to a harmonic

oscillator

Two macroscopic quantum systemsTwo macroscopic quantum systems

Flux-qubit entangled with the LC-oscillator

Qubit, two-level systemQubit, two-level system LC-harmonic oscillatorLC-harmonic oscillator

microwave fieldmicrowave field

|0|0, |1, |1 |0|0, |1, |1, ..., , ..., |N|N

hhpp

hFhFLLMIMIqqIIcirccirc

..

..

..

IIqubitqubit, , LCLC>>

00

10

20

21

11

01 Blue sidebandBlue sideband

Red sidebandRed sideband

-pulse-pulse

Marking the lateral sidebands

qubit Larmor frequency 13.96 GHzqubit Larmor frequency 13.96 GHz

-pulse length is determined by Rabi exp.-pulse length is determined by Rabi exp.

|10|11

|01

|00

|10|11

|01|00

spectroscopy after or without a spectroscopy after or without a -pulse -pulse 0 10 20 30 40 50

50

60

70

switc

hing

pro

babi

lity

[ %

]

Microwave pulse length [ ns ]

-pulse-pulseQubit Qubit

Rabi oscillationsRabi oscillations

70

60

50

40

30Sw

itchi

ng p

roba

bilit

y [%

]

2018161412108RF frequency [GHz]

after -pulse

without RF pulse

blue sideband 18.3 GHz

qubit 13.96 GHz

-10 dBm

red sideband 9.65 GHz

Red sideband Rabi oscillations |10Rabi oscillations |10 |01 |01 for various powers, for various powers,

after a after a pulse |00 pulse |00 |10 |10

|10|11

|01|00

|1010+ |01+ |01

Driven, off-resonance, vacuum Rabi oscillations

Sw

itchi

ng

pro

bab

ility

[%]

302010RF pulse width [ns]

-5

9.65 GHz 5 dBm

-3

3

1

-1

10 %

qubit Larmor frequency 13.96 GHz, oscillator frequency 4.31 GHz, qubit Larmor frequency 13.96 GHz, oscillator frequency 4.31 GHz,

red sidebandred sideband at 9.65 GHz at 9.65 GHz

Blue sideband qubit Larmor frequency 13.96 GHz, oscillator frequency 4.19 GHz, qubit Larmor frequency 13.96 GHz, oscillator frequency 4.19 GHz,

blue sidebandblue sideband at 18.15 GHz at 18.15 GHz

|10|11

|01|00

|0000+ |11+ |11

|10|11

|01|00

conditional dynamicsconditional dynamics

|11

Sw

itchi

ng p

roba

bilit

y [%

]

302010RF pulse width [ns]

18.28 GHz

8

8

7

6

5

10 %

9

10

after -pulse

after 2-pulse

dbm

C=10 pF, L=0.14 nH p = 4.3 GHz ~ 200 mK >> kBT~20 mK

LC-plasma mode LC-plasma mode 　　　　　　　　　　 qubit qubit 　　　　　　　　　　 cocouplingupling

Flux-qubit LC-oscillator systemFlux-qubit LC-oscillator systemPoster: J. Johansson

for cavity QED ( ENS Paris )for cavity QED ( ENS Paris )

Single mode cavitySingle mode cavity

Qubit n=50, 51Qubit n=50, 51

Sw

itchi

ng p

roba

bilit

y [%

]


Sw

itchi

ng p

roba

bilit

y [%

]


14GHz, -3dBm

10.25GHz, -14dBm qubit Rabi oscillation qubit Rabi oscillation pulspulsee

22pulspulsee

-, 2-, 2-pulse determined from Rabi -pulse determined from Rabi oscillationsoscillations

20 mK20 mK

J. Johansson et al., in preparation

spectroscopy under weak excitations

anti-crossingis observed

with help of thewith help of thedumping pulsedumping pulse

|e0

|e1

|g1|g0

readout readout qubit state qubit state

excite qubit excite qubit by aby a-pulse-pulse

1 → 21 → 2 3 ⇔ 43 ⇔ 4

shift qubit shift qubit adiabaticallyadiabatically

|e0

|e1

|g1|g0

|e0

|e1

|g1|g0

2 → 32 → 3

|g0

|g１

|e0

4

shift qubit shift qubit adiabaticallyadiabatically

I I qubitqubit, , LC-oscillator LC-oscillator >> 　　Vacuum Rabi : measurement schemeVacuum Rabi : measurement scheme

Vacuum Rabi oscillationsVacuum Rabi oscillationsDirect evidence of level quantization in a 0.1 mm large

superconducting macroscopic ＬＣ -circuit

J. Johansson et al., submitted

Influence of higher level occupationInfluence of higher level occupation

J. Johansson et al., submitted

connection to cavity QEDconnection to cavity QED

qubit 1qubit 1 qubit qubit 22

・・・・・・・・・・・・

・・・・・・

: Josephson junction

Control signal ： RF line

readoutSQUID

for qubit 2

qubit 2qubit 2

LC-resonator as a qubit coupler

Multi qubit operation schemeMulti qubit operation scheme

readoutSQUIDfor

qubit 1

qubit 1qubit 1

Harmonic oscillator

Map Map-1

qubit 1

harmonic oscillator

qubit 2

( b1 )0

( b1 )

(c)

0

(c)

( b2 )0

( b2 )√

qubit 1

qubit 2

|g, 0> |g, 1>

|g, 2>

|e, 0> |e, 1>

|e, 2>

(a)(a)

(b)(b)

(c)

( b2 )0

( b2 )√

phaseangle

Coupled Flux QubitsCoupled Flux Qubits

•Multi-photon Rabi oscillationMulti-photon Rabi oscillation - between Macroscopically distinct states- between Macroscopically distinct states

• Faster (Faster (,,-control -control To make best use of the coherence timeTo make best use of the coherence time

- - -control : Rabi with strong driving -control : Rabi with strong driving - - -control by composite pulse : Z(-control by composite pulse : Z()=X()=X(/2)Y(/2)Y()X(-)X(-/2)/2)

• Coupling between qubit and LC-oscillatorCoupling between qubit and LC-oscillator - Conditional spectroscopy of the coupled system - Conditional spectroscopy of the coupled system - Entanglement with an external oscillator- Entanglement with an external oscillator - - Vacuum Rabi oscillationsVacuum Rabi oscillations• Generation of “two qubit”-like states Generation of “two qubit”-like states

|00|00 + + |11|11 andand |01|01 + + |10|10

SummarySummary

Flux-qubit, Atom chip team at NTT-BRL Atsugi

MS+S2006 at NTT AtsugiFebruary 27-March 2, 2006

Int. Symp. on Mesoscopic Superconductivity & Spintronics

~ In the light of quantum computation ~

http://www.brl.ntt.co.jp/event/ms+s2006/

MS+S2004, March 2004

readout of superconducting flux qubits

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