Diapositive 1

1
Decoherence of a qubit -during free evolution
-during driven evolution -at readout
A -meter
Daniel ESTEVE
of Michel DEVORET
SPEC
YALE
2
DECOHERENCE DURING FREE EVOLUTION
dephasing
DEPHASING
3
The quantronium 1) a split Cooper pair box
1 d of freedom
4
2) protected from dephasing
energy (kBK)
n01(GHz)
d/2p
d/2p
Ng
Ng
EJ0.86 kBK EC0.68 kBK
5
Readout of persistent currents with dc
switching
3) with a readout junction
d/2p
Ng
6
Qubit control Rabi precession
rotation wRabi aURF
7
Readout fidelity ?
40 contrast (only)
8
Qubit manipulation  
arbitrary transformations
adiabatic frequency pulses for Z rotations
robust transformations
Composite   p    CORPSE   60X 300-X 420 X
  p     CORPSE
Single pulse
9
Decoherence sources in the quantronium circuit
d
10
Decoherence in the Quantronium
d
Relaxation
P0
if balanced junction !
11
Model for dephasing charge and phase noise
d
DNg ou Dd
(linear coupling)
Spectral density
12
Relaxation of the Quantronium
P0
T10.5µs
T1 0.3-2 ms
13
Ramsey interferences
Ramsey interferences reveal decoherence of
free evolution during the delay
14
Characterizing dephasing 1) decay of Ramsey
fringes
best ones
nRF 16409.50 MHz
15
typical sample

Fit with the linked cluster expansion static
approximation ( Makhlin Shnirman, Paladino,
Falci)
16
Comparing fits
static approximation ( Makhlin Shnirman,
Paladino, Falci)
Simple exponential
gaussian noise model
500 ns
17
away from optimal point
Coherence time
0.028
0.028
0.028
18
Characterizing dephasing 2a) phase detuning
pulses
Dt1
p/2X
p/2X
Dt2
19
Characterizing dephasing 2b) detuning charge
pulses
20
Characterizing decoherence 3) resonance linewidth
21
5) Probing the dynamics spin echo experiments
22
Direct mapping of echo amplitude
low frequency noise
23
Echo decay away from optimal point
24
Comparison exp vs model noise
spectral densities
non gaussian character of noise ??
Conclusion decay times ok, not time dependence
See G. Ithier et al. Decoherence in a quantum
bit Superconducting circuit circuit,
preprint
25
Closer look at charge and phase spectral
densities
Phase noise
Charge noise
Partly external
Cut-off at .5 MHz
26
Decoherence driven evolution versus free
evolution
Bloch-Redfield description
Free
See preprint on decoherence G. Ithier et al.
27
Spin locking
Determination of T1
28
Determination of T2
Decay of Rabi oscillations with Rabi frequency
29
Decay of Rabi oscillations with frequency
T2 480 ns
30
decoherence in the rotating frame ?
lab frame
Ramsey decay
T2300ns
rotating frame
T2480 ns
Conclusion more robust qubit encoding in the
rotating frame
31
Decoherence at readout projection fidelity ?
ideal QND readout
Readout 1
Readout 0
errors wrong answer projection error
A -meter
32
Decoherence dc versus rf readout
dc readout
V
resets the qubit
dc pulse
? switching

• simple, but
• rep rate limited by quasiparticles
• qubit reset NOT QND

33
Decoherence dc versus rf readout
PULSE IN
rf readout (M. Devoret, Yale)
PULSE OUT
U
d
RF pulse
dc pulse
? switching
? d dynamics in anharmonic potential

• simple, but
• -fidelity 40
• qubit reset NOT QND

more complex, but -better fidelity ? -no
reset possibly QND
34
Phase oscillations in a state dependent
anharmonic potential
(I. Siddiqi et al., PRL 93, 207002 (2004))
Qubit control port
The Josephson Bifurcation Amplifier
latching
OSCILLATION AMPLITUDE
MICROWAVE DRIVE AMPLITUDE
35
Microwave readout setup
MicroWave Generator
RFin
LO
V
demodulator
300 K
S
G40dB
M
Pulsing
I
Q
Vg
TN2.5K G40dB
-20dB
4 K
-20dB
LP 3.3GHz
-30dB
-30dB
600 mK
1 kW
4 kW
20 mK
LP 2GHz
HP 1.3GHz
Directionnal coupler
50 W
50 W
Sample from Yale
36
frequency 1.4GHz
Rabi oscillations
5ns
Readout contrast?
Bifurcation probability
P
Pulse duration (ns)
Microwave power (dBm, top)

(best dc switching 60)
Readout 50 contrast (Yale 60)
37
QND readout ?
p pulse on qubit
no pulse on qubit
Readout 1
Readout 1
Readout 2
OR
analysis yields for a single readout
Answer 1
Answer 0
Answer 1
Answer 1
Answer 0
Answer 0
partially QND
(Yale Saclay)
38
QND readout with an ac drive at optimal point ?
flux qubit
charge qubit
quantronium
box capacitance
SQUID inductance
JBA
Yale Saclay
TU Delft, Helsinki (for SSET)
partially QND
Chalmers
(in progress)
Readout fidelity QND readout are (still)
issues
39
This work on
the
Quantronium
dc
gate
dc
gate
µw
qp
box
trap
A -meter
readout
junction
1µm
SPEC
Appl. Physics
YALE
I. SIDDIQI F. PIERRE E. BOAKNIN L. FRUNZIO
G. ITHIER E. COLLIN P. ORFILA P. SENAT P.
JOYEZ D. VION P. MEESON D. ESTEVE
A. SHNIRMAN G. SCHOEN Y. MAKHLIN F. CHIARELLO
R. VIJAY C. RIGETTI M. METCALFE M. DEVORET
Karlsruhe Landau
Roma
remind 10-4 error rate on qubit gates, QND
useful but not mandatory
40
Yale quantronium sample
2mm
41
Qubit in ground state
42
Quantum Non-Demolition Fraction
? pulse
Readout 1 (R1)
Readout 2 (R2)
5ns
100ns
20ns
125ns
20ns
30ns
Ps(R1)
Ps(R2)
Ps(R1?R2)
Ps(R2/R1)
17.6
13.3
3.3
18.8
no ? pulse
? pulse
61.3
28.0
19.1
31.1
T11.3 ?s
QND Frac. ?