High fidelity Josephson phase qubits winning the war (battle…) on decoherence “Quantum...
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High fidelity Josephson phase qubits winning the war (battle…) on decoherence
• “Quantum Integrated Circuit” – scalable
• Fidelity breakthrough: single-shot tomography
• Tunable qubit – easy to use
• Two qubit gates – new results
Collaboration with NIST – Boulder
UC Santa Barbara
John MartinisAndrew ClelandRobert McDermottMatthias Steffen(Ken Cooper)Eva WeigNadav Katz
PDGS
Markus AnsmannMatthew NeeleyRadek BialczakErik Lucero
The Josephson JunctionSC
SC
~1nm barrier
Silicon or sapphire substrate
SiNx insulatorAl top electrode
Al bottom electrode
AlOx tunnel barrier
Josephson junction
2 = i2e
1 = i1e
IJ = I0 sin
V = (0 / 2) .
“Josephson Phase”
= 1 - 2
Qubit: Nonlinear LC resonator
23
2/3
000 /1
24II
IU
C
4/1
0
2/1
0
0
122
III
p
I RCLJ
Lifetime of state |1>
0 50.7
0.8
0.9
1
pU
10
2132
pn
nE
E /
1
RC
Up
U()<V> = 0
<V> pulse(state measurement)
I0
= 0/2I0cos nonlinear inductor
I cos I 0j V ) (1/L J
0 sin I I
LJ
2
V 0
1: Tunable well (with I)2: Transitions non-degenerate3: Tunneling from top wells4: Lifetime from R
E0
E1
E2
0
1
2n
n+11000~
Superconducting QubitsPhase Flux Charge
Ce
I
E
E
C
J
2/
2/2
00
104 102 1
Area (m2): 10-100 0.1-1 0.01
Potential &wavefunction
EngineeringZJ=1/w10C 10 103 105
Yale, Saclay, NEC, Chalmers
Delft, BerkeleyUCSB, NIST,Maryland
Josephson-Junction Qubit
|0>
|1>
• State PreparationWait t > 1/ for decay to |0>
• Qubit logic with bias control
• State Measurement: U(I+Ipulse) Single shot – high fidelity
Apply ~3ns Gaussian Ipulse
I pulse (lower barrier)
I = Idc + Idc(t) + Iwc(t)cos10t + Iws(t)sin10tphase
pote
ntia
l
) 2/(
)2(
z
wsy
wcx
I
IH
Idc(t) dcIE /10
2/)2/( 2/110C
2/)2/( 2/110C
1.0
0.8
0.6
0.4
0.2
0.00.80.70.60.50.40.30.2
|0>|1>|2>
Ipulse
Pro
b. T
unne
l
96%
|0> : no tunnel
|1> : tunnel
The UCSB/NIST Qubit
1
01
Idc
Qubit
Flux bias
1 0
Iw
VSQ
SQUID
microwave drive
Qubit
Flux bias
SQUID
ExperimentalApparatus
V source
20dB 4K
20mK
300K
I-Q switch
Sequencer & Timer
waves
IsIVs
fiber optics rf filters
w filters
~10ppm noise
V source~10ppm noise
20dB
20dB
Z, measure
X, Y
Ip
Iw
Is
Itime
Reset Compute Meas. Readout
Ip
Iw
Vs
0 1
X Y
Z
Repeat 1000x prob. 0,1
10ns
3ns 20dB
Spectroscopy
Bias current I (au)
10/ U
saturate
Ip
Iw
meas.
Mic
row
ave
fre
que
ncy
(G
Hz)
10(I)
26
few TLS resonances
P1 = grayscale
Qubit Fidelity TestsRabi:
Ramsey:
Echo:
T1:
Pro
bab
ility
1 s
tate
Large Visibility! T1 = 110 ns, T ~ 85 ns
~90% visibility
State Tomography
|0 |1
|0+ |1 |0+ i|1
y
x
X,Y
P1state tomography
• Good agreement with QM• Peak position gives state ), amplitude gives coherence
DAC-Q (X)
DA
C-I
(Y
)
|0
|1
X
Y
|0+|1
|0+i|1
Standard State Tomography (I,X,Y)
time (ns)
P1
I,X,Y
I
XY
0
1
10 10 i
|0+|1
State Evolution from Partial Measurement
tomography & final measurestate
preparation
15 ns 10 ns
|0+|1
Needed tocorrect errors.
First solid-stateexperiment.
N
p 110f
2
10i
partial measure p
Prob. = p/2“State tunneled”
Prob. = 1-p/2
|0
Iw
Ip
p
t
Theory: A. Korotkov, UCR
Partial Measurement
|0+|1
|0
pm
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Partial measurement probability p
Pol
ar a
ngle
M
(ra
d)
0 0.2 0.4 0.6 0.8 1 1.2Measure pulse amplitude V
max(V)
Azi
mut
hal r
otat
ion M
(ra
d)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.4
0.6
0.8
1
Partial measurement probability p
Nor
mal
ized
vis
ibili
ty
-30
-10
-20
0
/4
/2
3/4
p=0.25
p=0.75
Decoherence and Materials Im
{}/
Re
{}
=
= 1
/Q
<V2>1/2 [V]
future a-
Dielectric loss in x-overs
Where’s theproblem?
TLS in tunnel barrier
Two Level States(TLS)
New design
Theory: Martin et alYu & UCSB group
xtal Al2O3
a-Al2O3
New Qubits
60 m
SiNx capacitor
I: Circuit II: Epitaxial Materials
(loss of SiNx limits T1)
Al2O3
(substrate)
Al2O3
Re
Al
LEED:
Bias current I
wav
e fr
eq.
(GH
z)
Spectroscopy: epi-Re/Al2O3 qubit
~30x fewer TLS defects!
(NIST)
Long T1 in Phase Qubits
tRabi (ns)
UCSB/NIST
T1 = 500 ns
Rabi
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200 250 300 350 400
t [ns]
P |
1>
P1
(p
roba
bili
ty)
tRabi (ns)
These results:Conventional design
(May 2005):
• High visibility more useful than long T1
• T1 will be longer with better C dielectric
Future ProspectsCoherence
T1 > 500 ns in progress, need to lengthen T
STOP USING BAD MATERIALS!
Single Qubit operations work well
Coupled qubit experiment in DR
Simultaneous state measurement demonstrated
Bell states generated
Violate Bell’s inequality soon
Tunable qubit : 4+ types of CNOT gates possible
Scale-up infrastructure (for phase qubits)
Very optimistic about 10+ qubit quantum computer
Dielectric Loss in CVD SiO2
6.02 6.03 6.04 6.05 6.06 6.0710
-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
Frequency [GHz]
Pou
t [m
W]
f [GHz]
Po
ut [m
W]
Im{
}/R
e{
} =
=
1/Q
Pin lowering
HUGE DissipationC
L
<V2>1/2 [V]
Pin Pout
T = 25 mK
Theory of Dielectric Loss
Im{
}/R
e{
} =
=
1/Q
<V2>1/2 [V]
Two-level (TLS) bath: saturates at high power, decreasing loss
high power
Amorphous SiO2
von Schickfus and Hunklinger, 1977
E
Bulk SiO2: OHCi
3103 i %1OH C
SiO2 (no OH)
SiO2 (100ppm OH)
Theory of Dielectric Loss
Im{
}/R
e{
} =
=
1/Q
<V2>1/2 [V]
• Spin (TLS) bath: saturates at high power, decreasing loss
high power
Amorphous SiO2
von Schickfus and Hunklinger, 1977
E
Bulk SiO2: OHCi
3103 i %1OH C
SiNx, 20x better dielectricWhy?
Junction Resonances = Dielectric Loss at the Nanoscale
20
10
00.01 0.1 1
10.5
10.0
qubit bias (a.u.) splitting size S' (GHz)
N/G
Hz
(0.0
1 G
Hz
< S
< S
')
wav
e fr
eque
ncy
(GH
z)
13 m2
70 m2
13 m2
S/h
70 m2
avg. 5 samples:
New theory (suggested by I. Martin et al):
e d 1.5 nm
Al
Al
AlOx
S
SSA
dEdS
Nd 2/12max
2 ])/(1[
theory
CeEd
S 2/2nm5.1
210max
d=0.13 nm (bond size of OH defect!)Explains sharp cutoff
Smax in good agreement with TLS dipole moment:Charge (not I0) fluctuators likely explanation of resonances
2-level states(TLS)
.
Junction Resonances: Coupling Number Nc
0
10
2max
2
0
1
)ns 10/1(
/
)6/(
2
2 max
A
E
AS
dSS
S
A
i
S
0
1
qubit junction resonances …
Nc >> 1, Fermi golden rule for decay of 1 state:
2
max
2/
2/0
m 90/
10
10
max
A
AS
dEdSS
AN
SE
SE
S
c
Number resonances coupled to qubit:S
g
e
Statistically avoid withNc << 1 (small area)
Same formula for i as bulk dielectric loss
Implies i = 1.6x10-3, AlOx similar to SiOx (~1% OH defects)
E10
State Decay vs. Junction Area Monte-Carlo QM simulation:(-pulse, delay, then measure)
1.0
0.5
0.0100500
time (ns)
pro
ba
bili
ty P
1
A=2500 um2 (Nc=5.3)
A=260 um2 (Nc=1.7)
State Decay vs. Junction Area Monte-Carlo QM simulation:(-pulse, delay, then measure)
1.0
0.5
0.0100500
time (ns)
pro
ba
bili
ty P
1
A=2500 m2 (Nc=5.3)
A=260 m2 (Nc=1.7)
A=18 m2 (Nc=0.45)
Nc2/2
Need Nc < 0.3 (A < 10 m2) to statistically avoid resonances~ ~
State Measurement and Junction Resonances
)exp(
])/(2/exp[
1
102
1
p
iii
t
dtdESP
0
1
qubit junction resonances …
Nc’ >> 1, Landau-Zener tunneling:
2
210'
m1.0
mGHz 36.0
/
A
AhENc
Number resonances swept through:
tp
Couple to more resonances
With tp ~ 10 ns, explains fidelity loss in measurement!(10 ns)-1