Transcript Josephson-Junction “Atoms” for Quantum Computation

High fidelity Josephson phase qubits
winning the war (battle…) on decoherence
UC Santa Barbara
John Martinis
PD
Andrew Cleland
Robert McDermott
Matthias Steffen
(Ken Cooper)
Eva Weig
Nadav Katz
Collaboration with
NIST – Boulder
GS
Markus Ansmann
Matthew Neeley
Radek Bialczak
Erik Lucero
• “Quantum Integrated Circuit” – scalable
• Fidelity breakthrough: single-shot tomography
• Tunable qubit – easy to use
• Two qubit gates – new results
The Josephson Junction
i1
1 = e
SC
~1nm barrier
SC
i2
2 = e
Al top electrode
AlOx tunnel
barrier
“Josephson Phase”
 = 1 - 2
SiNx insulator
Al bottom
electrode
.
V = ( / 2) 
0
IJ = I0 sin 
Josephson junction
Silicon or sapphire
substrate
Qubit: Nonlinear LC resonator
I
R
I0
LJ
I = I 0 sin 
0

V=
2
C
I j = I0 cos  
 (1/L J) V
LJ = 0/2I0cos 
nonlinear inductor
U()
E2
E1
E0
G1
g10
DU
wp
4 2 I 0 0
DU =
3 2
[ 1- I / I0 ]

 
w p =  2 2 I 0 
 0 C 
1/ 2
g10
G0
[ 1 - I I0 ]
(En+1 - En )/ w p
Gn+1
~ 1000
G
G2 n
<V> = 0
1
0.9
w10
0.8
<V> pulse
3/ 2
(state measurement)
1/ 4
@ 1 RC Lifetime of state |1>
0.7
0
w21
w32
DU w p
5
1: Tunable well (with I)
2: Transitions non-degenerate
3: Tunneling from top wells
4: Lifetime from R
Superconducting Qubits
Phase
UCSB, NIST,
Maryland
Flux
Delft, Berkeley
Charge
Yale, Saclay,
NEC, Chalmers
E J I 0  0 / 2
= 2
EC
e / 2C
104
102
1
Area (mm2):
10-100
0.1-1
0.01
10 W
103 W
105 W
Potential &
wavefunction
Engineering
ZJ=1/w10C
• State Preparation
Wait t > 1/g10 for decay to |0>
• Qubit logic with bias control
I = Idc + Idc(t) + Imwc(t)cosw10t + Imws(t)sinw10t
potential
Josephson-Junction Qubit
|1>
|0>
H ( 2) = s x  I mwc ( / 2w10C) / 2
+ s y  I mws  ( / 2w10C)1/ 2 / 2
phase
1/ 2
+ s z  Idc(t)  (E10 /Idc )/ 2
Single shot – high fidelity
Apply ~3ns Gaussian Ipulse
|1> : tunnel
|0> : no
tunnel
1.0
Prob. Tunnel
• State Measurement: DU(I+Ipulse)
0.8
|0>
|1>
|2>
0.6
96%
0.4
0.2
0.0
0.2
0.3
0.4
0.5
0.6
Ipulse
I pulse (lower barrier)
0.7
0.8
The UCSB/NIST Qubit
Qubit
microwave
drive
Idc
Flux
bias
Im
Qubit
SQUID
w
VSQ
Flux
bias
1
0
w01
1 0
SQUID
Sequencer
& Timer
~10ppm noise
fiber optics
V source
~10ppm noise
Z, measure
mwaves
I Is Vs 300K
V source
X, Y
I-Q
switch
Ip
Imw
20dB
Experimental
Apparatus
X
Imw
Y
Z
Ip
Reset
Compute
20dB
20dB
20dB
3ns
Meas. Readout
time
Repeat 1000x
prob. 0,1
Is
01
4K
20mK
10ns
I
Vs
rf
filters
mw
filters
Spectroscopy
6
DU / w10
2
Imw
saturate
Ip
meas.
Microwave frequency (GHz)
P1 = grayscale
few TLS resonances
w10(I)
Bias current I (au)
Qubit Fidelity Tests
t
Rabi:
Ramsey:
T1:
t
Probability 1 state
Echo:
~90% visibility
t
t
Large Visibility! T1 = 110 ns, T ~ 85 ns
State Tomography
P1
state
tomography
|0
X,Y
|1
DAC-I (Y)
|0
x
|1
y
DAC-Q (X)
|0+ |1
|0+ i|1
|0+|1
X
|0+i|1
Y
• Good agreement with QM
• Peak position gives state (q,),
amplitude gives coherence
Standard State Tomography (I,X,Y)
X
I,X,Y
Y
P1
|0+|1
I
time (ns)
0
0 +i 1
0 +1
1
State Evolution from Partial Measurement
|0
Needed to
correct errors.
First solid-state
experiment.
i =
Theory: A. Korotkov, UCR
|0+|1
f =
0 +1
N
“State tunneled”
2
state
preparation
0 + 1- p 1
partial
measure p
Prob. = 1-p/2
Prob. = p/2
tomography & final measure
Imw
p
Ip
t
15 ns
10 ns
Partial Measurement
|0
Polar angle q (rad)
M
|0+|1
/2
/4
0
Azimuthal rotation  (rad)
M
p
Normalized visibility
qm
3/4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Partial measurement probability p
0.8
0.9
1
0
p=0.25
-10
p=0.75
-20
-30
0
0.2
0.4
0.6
0.8
1
Measure pulse amplitude Vmax (V)
1
1.2
0.8
0.6
0.4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Partial measurement probability p
0.8
0.9
1
Decoherence and Materials
Theory: Martin et al
Yu & UCSB group
Two Level States
(TLS)
Im{e}/Re{e} =  = 1/Q
Dielectric loss in x-overs
Where’s the
problem?
TLS in tunnel barrier
a-Al2O3
future a-
New design
xtal Al2O3
<V2>1/2 [V]
New Qubits
I: Circuit
II: Epitaxial Materials
LEED:
Al
Al2O3
Re
Al2O3
(substrate)
SiNx
capacitor
60 mm
(loss of SiNx limits T1)
mwave freq. (GHz)
Spectroscopy: epi-Re/Al2O3 qubit
(NIST)
~30x fewer
TLS defects!
Bias current I
Long T1 in Phase Qubits
Rabi
1
These results:
Conventional design
(May 2005):
P |1>
P1 (probability)
0.9
0.8
UCSB/NIST
0.7
0.6
0.5
0.4
0.3
0.2
T1 = 500 ns
0.1
0
0
50
100
150
200
250
300
350
400
tRabi (ns)
t [ns]
• High visibility more useful than long T1
• T1 will be longer with better C dielectric
tRabi (ns)
Future Prospects
Coherence
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
Pin
Pout
HUGE Dissipation
C
T = 25 mK
-7
10
Pin
lowering
-8
10
-10
10
-11
10
P
out
[mW]
Pout [mW]
-9
10
-12
Im{e}/Re{e} =  = 1/Q
L
10
-13
10
-14
10
-15
10
6.02
6.03
6.04
6.05
Frequency [GHz]
f [GHz]
6.06
6.07
<V2>1/2 [V]
Theory of Dielectric Loss
E
Two-level (TLS) bath: saturates
at high power, decreasing loss
high
power
von Schickfus and Hunklinger, 1977
Bulk SiO2:
 i  3 10-3
 i  COH
COH  1%
Im{e}/Re{e} =  = 1/Q
Amorphous SiO2
SiO2 (100ppm OH)
SiO2 (no OH)
<V2>1/2 [V]
Theory of Dielectric Loss
E
• Spin (TLS) bath: saturates at
high power, decreasing loss
high
power
von Schickfus and Hunklinger, 1977
Bulk SiO2:
 i  3 10-3
 i  COH
COH  1%
Im{e}/Re{e} =  = 1/Q
Amorphous SiO2
<V2>1/2 [V]
SiNx, 20x better dielectric
Why?
10.5
70
mm2
10.0
S/h
N/GHz (0.01 GHz < S < S')
mwave frequency (GHz)
Junction Resonances =
Dielectric Loss at the Nanoscale
70 mm2
20
avg. 5
samples:
13 mm2
10
13 mm2
qubit bias (a.u.)
0
0.01
0.1
1
splitting size S' (GHz)
New theory (suggested by I. Martin et al):
Al
2-level states
(TLS)
e. d
1.5 nm
AlOx
Al
[1 - ( S / S max ) 2 ]1/ 2
d 2N
= sA
dEdS
S
d
S max =
2 E10 e 2 / 2C
1.5nm
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
Junction Resonances: Coupling Number Nc
Number resonances coupled to qubit:
S
1
e
Nc @
S max

0
E10
g
0
junction resonances …
qubit
sA
S
dS
E10 + S / 2
 dE
E10 - S / 2
= sASmax
@ A / 90 mm 2
Statistically avoid with
Nc << 1 (small area)
Nc >> 1, Fermi golden rule for decay of 1 state:
2
G1 @

S max

0
sA  S 
2
  dS
S 2
2
= ( / 6)sASmax
=  i E10 / 
Same formula for i as bulk dielectric loss
@ (1 / 10 ns) A0
Implies i = 1.6x10-3, AlOx similar to SiOx (~1% OH defects)
State Decay vs. Junction Area
Monte-Carlo QM simulation:
(-pulse, delay, then measure)
probability P1
1.0
0.5
A=260 um2 (Nc=1.7)
0.0
0
A=2500 um2 (Nc=5.3)
50
time (ns)
100
State Decay vs. Junction Area
Monte-Carlo QM simulation:
(-pulse, delay, then measure)
Nc2/2
probability P1
1.0
A=18 mm2 (Nc=0.45)
0.5
A=260 mm2 (Nc=1.7)
0.0
0
A=2500 mm2 (Nc=5.3)
50
100
time (ns)
2) to statistically avoid resonances
Need Nc <
0.3
(A
<
10
mm
~
~
State Measurement and Junction Resonances
Number resonances swept through:
1
DE10 / h A
0.36 GHz mm 2
A

0.1mm 2
N c' @
tp
0
junction resonances …
qubit
Couple to more
resonances
Nc’ >> 1, Landau-Zener tunneling:
P1 @  exp[-Si2 / 2 (dE10 / dt) i ]
i
= exp(-G1t p )
(10 ns)-1
With tp ~ 10 ns, explains fidelity loss in measurement!