1. Readout of superconducting flux qubits
Frontiers in Quantum Nanoscience
A Sir Mark Oliphant & PITP Conference
Noosa Blue Resort, 24 January 2006
Readout of superconducting flux qubits
Hideaki Takayanagi
髙柳 英明
NTT Basic Research Laboratories
H. Tanaka, S. Saito, H. Nakano,
J. Johansson, F. Deppe,
T.Kutsuzawa,and K. Semba
NTT Basic Research Labs.
Tokyo University of Science
CREST JST
M. Ueda
Tokyo Institute of Technology
M. Thorwart
Heinrich Heine University
D. Haviland
KTH
Posters : Nakano (Berry Phase)
Johansson（Vacuum Rabi)

2. Sample size ～μm e-beam lithography Shadow evaporation Lift-off
Loop size
SQUID ~ 7 x 7 m2
qubit ~ 5 x 5 m2
Mutual inductance
M ~ 7 pH
Josephson junctions
Al / Al2O3 / Al
Junction area
SQUID : 0.1 x 0.08 m2
qubit : 0.1 x 0.2 m2,
( a = 0.7 )
5 m
IC(SQUID)~ 0.5 mA
IC(qubit)~ 0.7 mA
M Iq ISQ ~ 3.7 GHz

3. Multi-photon transition between
superposition of macroscopic quantum states ｰ
( ) /√2　1st excited state ＋
( ) /√2　ground state 3 3 2 2 1 1 3 1 2 2 1 3

4. Analogy of Schroedinger’s cat
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.
superposition of macroscopically distinct states
Qubit
Ground state
Qubit
Excited state
Resonant
microwave photon
Superconducting
persistent current ~ 0.5 mA
( ~ 106 cooper pairs )
Φext : magnetic flux

5. Multi-photon spectroscopy
Multi-photon transition
Multi-photon spectroscopy
S. Saito et al., PRL 93, (2004)
SQUID readout -2 -1 1 2
d I SW
(nA)
1.504
1.502
1.500
1.498
1.496 F
qubit /
RF : 3.8 GHz
-10 dBm １ 3
D=0.86GHz
1-photon
2 -photon 2 1 -1 -2
d I SW
(nA)
1.504
1.502
1.500
1.498
1.496 F
qubit /
RF : 3.8 GHz
0 dBm １ 3

6. Multiphoton Rabi
Observation of multiphoton Qubit control by microwave pulse.
Two colors
Two photons
Difference frequency
Single color Multi photon
Sum frequency
Two colors
Two photons
Sum frequency
Y. Nakamura, et al., PRL(2001)

7. RF pulse measurement RF pulse 70 ns 1200 ns ~100 nA 400 mV Vth
repetition:
3.3kHz ( ms)
|g>
|e>
measurement
RF pulse t
|g>
Ibias
70 ns
1200 ns
~100 nA
|e> t
Discrimination of the signal
Vmeas
|g>
400 mV
switching
Vth
|e>
Non-switching t

8. Single color & Multi photon
1-photon Rabi
2-photon Rabi
3-photon Rabi
4-photon Rabi
10.25GHz x 3

9. Two colors, Two photons & Sum frequency
10.25GHz, - 4dBm
10.25GHz, 4dBm
10.25GHz
16.2GHz

10. Two colors, Two photons & Difference frequency
18.5GHz, 0dBm
18.5GHz, 8dBm
11.1GHz
18.5GHz

11. Discussion Assume that the microwave is in the coherent state as
is the solution of
The probability to find the state in the ground state is
With the conditions

12. Comparisions between experiments and calculations
Sum freq.
Difference freq.
a1 = [mV-1]
a2 =
a1 = [mV-1]
a2 =

13. Control Gates
Rabi Oscillation W: Quantum bit oscillates between and with a
frequency that is proportional to the amplitude of irradiated microwave.
Any multiple qubit logic gate may be composed
from CNOT and single qubit gates.
p pulse：width of p/W
Rotation Gate
p/2 pulse
Controlled-not gate A A’ B B’ +
A B A’B’
When A=1,
B is reversed.

14. Control of two angles in Bloch sphere q（Rabi）and （Ramsey） 
(t)
latitude
Control of
Ｒａｂｉ
longitude
Control of
by introduce detuning
Ramsey
by phase shift
※ in a rotating frame
π/2
Pulse
π/2
Pulse

15. Phase shift without detuning
Detuning method vs. Phase shift method
　with detuning t
π/2Pulse
⊿ｔ12
π/2Pulse Ψ
Equator
Phase shift without detuning t
π/2Pulse
⊿ｔ12
π/2Pulse Ψ
※ in a rotating frame

16. Advantage of Phase shift method
Ramsey （detuning method dｆ~0.2 GHz）
⊿Φ＝０
T=1/df～5ns
⊿Φ＝π/2
π/2
Pulse
π/2
Pulse
⊿Φ＝π
Ramsey （phase shift method dｆ=0 Hz）
T=1/fR～88ps
π/2
Pulse
π/2
Pulse
fR：RF ~ 11.4 GHz

17. Measurement scheme Ψ URF ⊿ｔ12 Read out voltage ｜１＞ ｜０＞ V
π/2
Pulse
π/2
Pulse
Read out voltage
｜１＞
｜０＞ V
ensemble：１0,000
T=25mK

18. ３. Fast Oscillation Resonant Frequancy １１．４[GHz]
Av：10,000 times
TPhaseShift=89 ps
Resonant Frequancy
１１．４[GHz]
π/2 pulse => ５ [ns]
Frequancy by fitting
11.18±0.01 [GHz]
Dephasing time
1.84[ns]
⊿Φ＝０
⊿Φ＝π/2
⊿Φ＝π
⊿Φ＝3π/2

19. We succeeded in observing Larmor precession ( 11.4 GHz )
of a flux qubit with phase shifted double pulse method.
　　An arbitrary unitary transformation of a single qubit is possible.
・ Advantage
＞We can control qubit phase rapidly ( ~ 10 GHz ).
　　　→　We can save time for each quantum-gate operation
　　　→　Compared with the detuning method (~ 0.1 GHz ),
10 ～ 100 times many gates can be implemented.

20. Artificial Atom in a Cavity
Cavity QED
I. Chiorescu et al, Nature 431, 159 (2004)
A. Wallraff et al, Nature 431, 162 (2004)

21. Three-fold m-metal shield Dilution refridgerator
Measurement system
E/M shielding (-100 dB) &
Three-fold m-metal shield
Dilution refridgerator
(~ 20 mK)
RF-line
Ibias-line
Vm-line
sample
package
RF-line
Ibias -line
Vm-line

22. Sample I bias V meas I bias V meas Csh Microwave line MW qubit
SQUID
On-chip component
[1] LC mode、filtering
　　capacitor( Csh )
resistor ( Ibias, Vmeas )
[2] strong driving：
　　microwave line
Microwave line

23. Coherent dynamics of a flux qubit coupled to a harmonic oscillator
Csh
Csh
Llead
Llead
Qubit
I bias
V meas
Microwave line
Two macroscopic quantum systems
Qubit coupled to a spatially separated LC-harmonic oscillator

24. Flux-qubit entangled with the LC-oscillator
Qubit, two-level system
LC-harmonic oscillator
|0, |1
|0, |1, ..., |N .
MIqIcirc
hFL
hwp
microwave field
Blue sideband
Red sideband
p -pulse
Iqubit, LC>

25. Marking the lateral sidebands
p-pulse
Qubit
Rabi oscillations
qubit Larmor frequency GHz
p-pulse length is determined by Rabi exp.
spectroscopy after or without a p-pulse
|10
|11
|01 p
|00

26. Red sideband |11 |10 p |01 |00
Rabi oscillations |10  |01 for various powers,
after a p pulse |00  |10
qubit Larmor frequency GHz, oscillator frequency 4.31 GHz, red sideband at 9.65 GHz
|10
|11
|01
|00 p
|10+ |01
Driven, off-resonance, vacuum Rabi oscillations

27. Blue sideband |11 |10 |01 |00 |10 |11 |01 |00 p 2p
qubit Larmor frequency GHz, oscillator frequency 4.19 GHz, blue sideband at GHz
|11
|10
|00+ |11
after p-pulse
|01
|00
after 2p-pulse
|10
|11
|01
|00 p
conditional dynamics
dbm 2p
|11

28. Flux-qubit LC-oscillator system
Poster: J. Johansson
LC-plasma mode 　　 　 　　qubit 　　　　　 coupling
C=10 pF, L=0.14 nH  np = 4.3 GHz ~ 200 mK >> kBT~20 mK

29. for cavity QED ( ENS Paris )
Qubit n=50, 51
Single mode cavity

30. p-, 2p-pulse determined from Rabi oscillations
qubit Rabi oscillation
10.25GHz, -14dBm
14GHz, -3dBm
20 mK
2p pulse

31. J. Johansson et al., in preparation
spectroscopy
under weak
excitations
anti-crossing
is observed
with help of the
dumping pulse
J. Johansson et al., in preparation

32. Vacuum Rabi : measurement scheme
|g1
|g0 p
I qubit, LC-oscillator >　
|e0
|e1
|g1
|g0
|e1
|e0
|g1
2 → 3
|g0
excite qubit
by a p-pulse
shift qubit
adiabatically
shift qubit
adiabatically
readout
qubit state
3 ⇔ 4
1 → 2
|e0 4
|g１
|g0

33. Vacuum Rabi oscillations
Direct evidence of level quantization in a 0.1 mm large
superconducting macroscopic ＬＣ-circuit
J. Johansson et al., submitted

34. Influence of higher level occupation J. Johansson et al., submitted

35. connection to cavity QED

36. Multi qubit operation scheme
Control signal ：RF line
...
Harmonic oscillator
LC-resonator as a qubit coupler
readout
SQUID
for
qubit 1
readout
SQUID
for
qubit 2
・・・
・・・
qubit 1
qubit 2
・・・ n
: Josephson junction

37. |e, 2> |e, 1> (b) |e, 0> (c) |g, 2> (a) |g, 1>
qubit 1
Map
Map-1
harmonic oscillator
qubit 2
( b1 ) p
( b1 ) p
angle
qubit 1
phase
(c)
p/2
( b2 ) p
( b2 )
p/√
p/2
( b2 ) p
( b2 )
p/√
p/2
(c)
p/2 p 2 2
qubit 2

38. Coupled Flux Qubits

39. Summary Multi-photon Rabi oscillation
- between Macroscopically distinct states
Faster (q,j)-control  To make best use of the coherence time
- q-control : Rabi with strong driving
- j-control by composite pulse : Z(j)=X(p/2)Y(j)X(-p/2)
Coupling between qubit and LC-oscillator Conditional spectroscopy of the coupled system
- Entanglement with an external oscillator
- Vacuum Rabi oscillations
Generation of “two qubit”-like states
a|00 + b|11 and a|01 + b|10

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

41. MS+S2006 at NTT Atsugi February 27-March 2, 2006
Int. Symp. on Mesoscopic Superconductivity & Spintronics
~ In the light of quantum computation ~
MS+S2004, March 2004