Readout of superconducting flux qubits

1
Frontiers in Quantum Nanoscience A Sir Mark
Oliphant PITP Conference Noosa Blue Resort, 24
January 2006
Readout of superconducting flux qubits
Hideaki Takayanagi ??
?? 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
Multi-photon transition between superposition of
macroscopic quantum states
?
( ) /v2 1st excited state

( ) /v2 ground state
3
3
2
2
1
1
3
1
2
2
3
1
4
Analogy of Schroedingers 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 )
Fext magnetic flux
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Multi-photon transition
Multi-photon spectroscopy
S. Saito et al., PRL 93, 037001(2004)
SQUID readout
D0.86GHz
1-photon
2 -photon
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Multiphoton Rabi
Observation of multiphoton Qubit control by
microwave pulse.
Two colors Two photons Difference frequency
Two colors Two photons Sum frequency
Single color Multi photon Sum frequency
Y. Nakamura, et al., PRL(2001)
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repetition 3.3kHz ( 300 ms)
RF pulse
measurement
RF pulse
t
ggt
Ibias
70 ns
1200 ns
100 nA
egt
0
t
Discrimination of the signal
Vmeas
ggt
400 mV
switching
Vth
egt
0
Non-switching
t
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Single color Multi photon
1-photon Rabi
2-photon Rabi
3-photon Rabi
4-photon Rabi
10.25GHz x 3
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Two colors, Two photons Sum frequency
10.25GHz, - 4dBm
10.25GHz, 4dBm
10.25GHz
16.2GHz
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Two colors, Two photons Difference frequency
18.5GHz, 0dBm
18.5GHz, 8dBm
11.1GHz
18.5GHz
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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
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Comparisions between experiments and calculations
Sum freq.
Difference freq.
a1 0.00741mV-1 a2 0.0131
a1 0.0118 mV-1 a2 0.00911
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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 pulsewidth of p/W
Rotation Gate
p/2 pulse
Controlled-not gate
A
A
B
B

A B AB 0 0 0 0 0 1 0 1 1 0 1
1 1 1 1 0
When A1, B is reversed.
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Control of two angles in Bloch sphere
q(Rabi)and (Ramsey)
latitude
Control of
Rabi
longitude
Control of
by introduce detuning
Ramsey
by phase shift
? in a rotating frame
p/2 Pulse
p/2 Pulse
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Detuning method vs. Phase shift method
with detuning
t
?t12
p/2Pulse
p/2Pulse
Equator
Phase shift without detuning
t
p/2Pulse
p/2Pulse
?t12
? in a rotating frame
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Advantage of Phase shift method
Ramsey (detuning method df0.2 GHz)
?F0
T1/df5ns
?Fp/2
p/2 Pulse
p/2 Pulse
?Fp
Ramsey (phase shift method df0 Hz)
T1/fR88ps
p/2 Pulse
p/2 Pulse
fRRF 11.4 GHz
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Measurement scheme
?t12
p/2 Pulse
p/2 Pulse
Read out voltage
1gt
0gt
ensemble10,000
T25mK
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3. Fast Oscillation
Av10,000 times
TPhaseShift89 ps
Resonant Frequancy 11.4GHz
p/2 pulse gt 5 ns
Frequancy by fitting 11.180.01 GHz
Dephasing time 1.84ns
?Fp
?F0
?Fp/2
?F3p/2
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• 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 gtWe 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.
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Artificial Atom in a Cavity
Cavity QED
A. Wallraff et al, Nature 431, 162 (2004)
I. Chiorescu et al, Nature 431, 159 (2004)
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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
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Sample
V meas
I bias
I bias
V meas
Csh
MW
On-chip component 1 LC mode?filtering
capacitor( Csh ) resistor ( Ibias, Vmeas
) 2 strong driving microwave line
Microwave line
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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
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Flux-qubit entangled with the LC-oscillator
Qubit, two-level system
LC-harmonic oscillator
0?, 1?
0?, 1?, ..., N?
. . .
MIqIcirc
hFL
hwp
microwave field
Iqubit, LCgt
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Marking the lateral sidebands
Qubit Rabi oscillations

• qubit Larmor frequency 13.96 GHz
• p-pulse length is determined by Rabi exp.

• spectroscopy after or without a p-pulse

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Red sideband

• Rabi oscillations 10? ? 01? for various
  powers,
• 
  after a p pulse 00? ?
  10?

• qubit Larmor frequency 13.96 GHz, oscillator
  frequency 4.31 GHz, red sideband at 9.65 GHz

Driven, off-resonance, vacuum Rabi oscillations
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Blue sideband

• qubit Larmor frequency 13.96 GHz, oscillator
  frequency 4.19 GHz, blue sideband at 18.15 GHz

11?
10?
00? 11?
after p-pulse
01?
00?
after 2p-pulse
dbm
11?
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Flux-qubit LC-oscillator system
Poster J. Johansson
LC-plasma mode qubit
coupling
C10 pF, L0.14 nH ? np 4.3 GHz 200 mK gtgt
kBT20 mK
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for cavity QED ( ENS Paris )
Qubit n50, 51
Single mode cavity
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p-, 2p-pulse determined from Rabi oscillations
qubit Rabi oscillation
10.25GHz, -14dBm
20 mK
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spectroscopy under weak excitations
anti-crossing is observed
with help of the dumping pulse
J. Johansson et al., in preparation
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Vacuum Rabi measurement scheme
I qubit, LC-oscillator gt
e1?
e0?
g1?
2 ? 3
g0?
readout qubit state
excite qubit by a p-pulse
shift qubit adiabatically
shift qubit adiabatically
3 ? 4
1 ? 2
e0?
4
g1?
g0?
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Vacuum Rabi oscillations
Direct evidence of level quantization in a 0.1 mm
large superconducting macroscopic LC-circuit
J. Johansson et al., submitted
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Influence of higher level occupation
J. Johansson et al., submitted
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connection to cavity QED
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Multi qubit operation scheme
Control signal RF line
LC-resonator as a qubit coupler


qubit 1
qubit 2

n
37
qubit 1
Map
Map-1
harmonic oscillator
qubit 2
( b1 ) p 0
( b1 ) p p
angle
phase
qubit 1
( b2 ) p 0
( b2 ) p 0
2
2
qubit 2
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Coupled Flux Qubits
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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
• a00? b11? and
  a01? b10?

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Flux-qubit, Atom chip team at NTT-BRL Atsugi
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MSS2006 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/mss2006/
MSS2004, March 2004