Transcript Coherence and decoherence in Josephson junction qubits

Coherence and decoherence in Josephson junction qubits
Yasunobu Nakamura, Fumiki Yoshihara, Khalil Harrabi
Antti Niskanen, JawShen Tsai
NEC Fundamental and Environmental Research Labs.
RIKEN Frontier Research System
CREST-JST
• Decoherence of qubit, bias dependence
• Tunable coupling scheme based on parametric coupling
using quantum inductance
Josephson junction qubits
small
large
Josephson energy = confinement potential
charging energy = kinetic energy  quantized states
Flux qubit
Phase qubit
Energy
Charge qubit
typical qubit energy
typical experimental temperature
Examples of Josephson junction qubits
charge qubit/NEC
flux qubit/Delft

2 mm
phase qubit/NIST/UCSB
charge qubit (quantronium)/Saclay
~100 mm
SQUID readout of flux qubit
qubit
+underdamped SQUID
~20 ns
To hold voltage state
after switching
SQUID
Ib pulse
~30 ns rise/fall time
~1 ms
0
1
qubit
switch
0
Switching probability (%)
100
time
w/o
-pulse
80
60
40
20
w/ -pulse
0
1.30
1.32
1.34
I bias (a.u.)
I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooij, Science 299, 1869 (2003)
1.36
Coherent control of flux qubit
Rabi oscillations
resonant
microwave pulse
visibility~79.5%
Study of decoherence
= Characterization of environment
environment
interaction
qubit
tunable
tunable
Possible decoherence sources
magnetic-field noise?
trapped vortices?
paramagnetic/nuclear spins?
charge fluctuations?
environment
circuit modes?
phonons?
quasiparticle
tunneling?
photons?
charge/Josephson-energy fluctuations?
Flux qubit: Hamiltonian and energy levels
Energy (GHz)
100
0
-100
0.8
1.0
q/
f/f*
J.E. Mooij et al. Science 285, 1036 (1999)
1.2
f*=0.5
Sensitivity to noises
relaxation
transverse coupling
dephasing
longitudinal coupling
Energy relaxation
relaxation and excitation
for weak perturbation: Fermi’s golden rule
• qubit energy E variable
• relaxation  S(+) and excitation  S(-)
 quantum spectrum analyzer
ex. Johnson noise in ohmic resistor R
zero-point
fluctuation of
environment
absorption
spontaneous
emission
T1 measurement
 ~ 4ns
Switching probability (%)
delay

readout pulse
80
70
60
50
0.0
0.4
0.8
Time ( ms)
1.2
1.6
initialization to ground state is better than 90%
 relaxation dominant
 classical noise is not important at qubit frequency ~ 5GHz
T1 vs f
 ~ 4ns
delay
readout pulse
1 vs E
• Data from both sides of
spectroscopy coincide
• Positions of peaks are not
reproduced in different samples
• Peaks correspond to
anticrossings in spectroscopy
assuming flux noise (not assured)
1 vs E: Comparison of two samples
sample3
sample5
Random high-frequency peaks. Broad low-frequency structure and high-frequency floor.
Dephasing
free evolution of the qubit phase
dephasing
for Gaussian fluctuations
sensitivity of qubit energy to the fluctuation
of external parameter
information of S() at low frequencies
Dephasing: T2Ramsey, T2echo measurement
Ramsey interference (free induction decay)
/2~2ns
/2
readout pulse
1
weight
t
0.8
0.6
0.4
0.2
0.01
0.1
1
freq.
10
100
spin echo
/2~2ns
/2
 ~ 4ns
readout pulse
t/2
1
weight
t/2
0.8
0.6
0.4
0.2
0.01
0.1
1
freq.
10
100
correspond to detuning
Optimal point to minimize dephasing
f
• two bias parameters
– External flux: f =ex/0
– SQUID bias current Ib
E (GHz)
f
G. Burkard et at. PRB 71, 134504 (2005)
Ib
T1 and T2echo at f=f*, Ib=Ib*
T1=54516ns
Echo decay time is
limited by relaxation
Pure dephasing due to
high frequency noise
(>MHz) is negligible
Echo at ff*, Ib=Ib*
assuming 1/f flux noise
do not fit
does not fit
2Ramsey, 2echo vs f
Red lines:
fit
For
for 3.17 mm2
cf. 7±3x10-6 [0] for 2500-160000 mm2 F.C.Wellstood et al. APL50, 772 (1987)
~1x10-4 [0] for 5.6 mm2 G.Ithier et al. PRB 72, 134519 (2005)
Optimal point to minimize dephasing
f
• two bias parameters
– External flux: f =ex/0
– SQUID bias current Ib
E (GHz)
f
Ib
T1, T2Ramsey, T2echo vs Ib
can be obtained experimentally
at Ib=Ib*
at |Ib-Ib*|=large
Echo at f=f*, IbIb*
at Ib=Ib*
at |Ib-Ib*|=large
-echo does not work
-exponential decay
 white noise (cutoff>100MHz)
exponential fit
Gaussian fit
Sammary
• T1, T2 measurement in flux qubit, T1,T2~1ms
• dependence on flux bias and SQUID-current bias condition
 characterization of environment
Optimal point f=f*, Ib=Ib*
f=f*, IbIb*
T1 limited echo decay
Pure dephasing due to low freq. noise
‘white’ Ib noise dominant
ff*, Ib=Ib*
1/f flux noise dominant
We do not understand yet
-T1 vs flux bias
-dephasing at optimal point
-origin of 1/f noise
Optimal point and quantum inductance
 current
•
 inductance
At optimal point
– Dephasing is minimal
– Persistent current is zero
•
•
Inductive coupling ~ xx; effective only for 12
Current readout should be done elsewhere
•
•
Depend on flux bias  tunable parametric coupling
Depend on qubit state  nondemolition inductance readout
– Quantum inductance is finite
Tunable coupling between flux qubits
•
•
Use nonlinear quantum
inductance of high-frequency
qubit3 as transformer loop
Drive the nonlinear
inductance at |1-2| and
parametrically induce
effective coupling between
qubit1 and qubit2
At the optimal point for qubit1 and qubit2
Effective coupling; can be zero at dc
Tunable coupling between flux qubits
• Advantages
– Qubits are always biased at
optimal point
– Coupling is proportional to
MW amplitude; can be
effectively switched off
– Induced coupling term also
has protection against flux
noise
|10
|01
|10
|01
Simulated time evolution vs.
control MW pulse width
Double-CNOT
within tens of ns
A.O. Niskanen et al., cond-mat/0512238
Simple demonstration of tunable coupling between flux qubits
•
Three qubits and a readout SQUID


1
t
|1-2|
|00  |10  |10+|01  |00+|11
readout
qubit3
qubit1
Psw
|00
qubit2
|11
t
Easy to distinguish |00 and |11 (not |01 and |10)
A.O. Niskanen et al., cond-mat/0512238
Future
Tunable coupling
Single qubit control
Nondemolition readout
Long coherence time