High fidelity Josephson phase qubits winning the war battle on decoherence

1
High fidelity Josephson phase qubits winning
the war (battle) on decoherence
UC Santa Barbara
John Martinis Andrew Cleland Robert
McDermott Matthias Steffen (Ken Cooper) Eva
Weig Nadav Katz
Collaboration with NIST Boulder
Markus Ansmann Matthew Neeley Radek Bialczak Erik
Lucero
PD
GS

• Quantum Integrated Circuit scalable
• Fidelity breakthrough single-shot tomography
• Tunable qubit easy to use
• Two qubit gates new results

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The Josephson Junction
SC
?1
Josephson Phase ? ?1 - ?2
1nm barrier
?2
SC
Josephson junction
Al top electrode
SiNx insulator
AlOx tunnel barrier
Al bottom electrode
Silicon or sapphire substrate
3
Qubit Nonlinear LC resonator
I
R
I0
C
LJ
U(d)
ltVgt 0
g10
DU
wp
ltVgt pulse (state measurement)
1 Tunable well (with I) 2 Transitions
non-degenerate 3 Tunneling from top wells 4
Lifetime from R
g10
_at_
1
Lifetime of state 1gt
RC
4
Superconducting Qubits
Phase
Flux
Charge
Yale, Saclay, NEC, Chalmers
UCSB, NIST, Maryland
Delft, Berkeley
102
1
104
Area (mm2)
10-100
0.1-1
0.01
Potential wavefunction
Engineering ZJ1/w10C
10 W
103 W
105 W
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Josephson-Junction Qubit

• State Preparation
• Wait t gt 1/g10 for decay to 0gt
• Qubit logic with bias control
• State Measurement DU(IIpulse)
• Single shot high fidelity
• Apply 3ns Gaussian Ipulse

potential
1gt
0gt
I Idc dIdc(t) Imwc(t)cosw10t
Imws(t)sinw10t
phase
0gt
1gt
2gt
96
Prob. Tunnel
1gt tunnel
0gt no tunnel
Ipulse
I pulse (lower barrier)
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The UCSB/NIST Qubit
Qubit
SQUID
microwave drive
Flux bias
Idc
I?w
Qubit
SQUID
VSQ
Flux bias
?1?
???
?01
1 ?0
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ExperimentalApparatus
Is
Vs
If
Sequencer Timer
300K
V source
10ppm noise
fiber optics
rf filters
V source
Ip
10ppm noise
Z, measure
Imw
X, Y
I-Q switch
mwaves
20dB
20dB
4K
20mK
mw filters
20dB
10ns
3ns
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Spectroscopy
2
6
P1 grayscale
saturate
Imw
few TLS resonances
Ip
meas.
Microwave frequency (GHz)
w10(I)
Bias current I (au)
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Qubit Fidelity Tests
90 visibility
t
Rabi
Ramsey
t
Probability 1 state
Echo
t
t
T1
Large Visibility! T1 110 ns, Tf 85 ns
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State Tomography
P1
state tomography
0?
1?
X,Y
0?
DAC-I (Y)
1?
DAC-Q (X)
0? i1?
0? 1?

• Good agreement with QM
• Peak position gives state (q,f),
• amplitude gives coherence

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Standard State Tomography (I,X,Y)
X
Y
I,X,Y
0?1?
P1
I
time (ns)
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State Evolution from Partial Measurement
0?
Needed to correct errors. First
solid-state experiment.
Theory A. Korotkov, UCR
0?1?
Prob. 1-p/2
State tunneled
Prob. p/2
state preparation
partial measure p
tomography final measure
I?w
p
Ip
t
15 ns
10 ns
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Partial Measurement
0?
qm
p
0?1?
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Decoherence and Materials
Theory Martin et al Yu UCSB group
Wheres the problem?
Two Level States (TLS)
Dielectric loss in x-overs
TLS in tunnel barrier
a-Al2O3
Ime/Ree d 1/Q
future a-
New design
xtal Al2O3
ltV2gt1/2 V
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New Qubits
I Circuit
II Epitaxial Materials
(NIST)
SiNx capacitor
60 ?m
(loss of SiNx limits T1)
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Long T1 in Phase Qubits
These results
Conventional design (May 2005)
UCSB/NIST
P1 (probability)
T1 500 ns
tRabi (ns)
tRabi (ns)

• High visibility more useful than long T1
• T1 will be longer with better C dielectric

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Future Prospects

• Coherence
• T1 gt 500 ns in progress, need to lengthen Tf
• STOP USING BAD MATERIALS!
• Single Qubit operations work well
• Coupled qubit experiment in DR
• Simultaneous state measurement demonstrated
• Bell states generated
• Violate Bells inequality soon
• Tunable qubit 4 types of CNOT gates possible
• Scale-up infrastructure (for phase qubits)

Very optimistic about 10 qubit quantum computer
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Dielectric Loss in CVD SiO2
Pin
Pout
HUGE Dissipation
C
L
T 25 mK
Pin lowering
Ime/Ree d 1/Q
Pout mW
ltV2gt1/2 V
f GHz
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Theory of Dielectric Loss
E
Amorphous SiO2
Two-level (TLS) bath saturates at high power,
decreasing loss
high power
Ime/Ree d 1/Q
SiO2 (100ppm OH)
von Schickfus and Hunklinger, 1977
Bulk SiO2
SiO2 (no OH)
ltV2gt1/2 V
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Theory of Dielectric Loss
E
Amorphous SiO2

• Spin (TLS) bath saturates at
• high power, decreasing loss

high power
Ime/Ree d 1/Q
von Schickfus and Hunklinger, 1977
Bulk SiO2
ltV2gt1/2 V
SiNx, 20x better dielectric Why?
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Junction Resonances Dielectric Loss at the
Nanoscale
New theory (suggested by I. Martin et al)
70 ?m2
70 ?m2
avg. 5 samples
Al
2-level states (TLS)
.
e d
1.5 nm
?wave frequency (GHz)
AlOx
N/GHz (0.01 GHz lt S lt S')
13 ?m2
Al
S/h
theory
13 ?m2
qubit bias (a.u.)
splitting size S' (GHz)
d0.13 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
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Junction Resonances Coupling Number Nc
Number resonances coupled to qubit
S
1
e
E10
g
0
Statistically avoid with Nc ltlt 1 (small area)
qubit
junction resonances
Nc gtgt 1, Fermi golden rule for decay of 1 state
Same formula for di as bulk dielectric loss
Implies di 1.6x10-3, AlOx similar to SiOx (1
OH defects)
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State Decay vs. Junction Area
Monte-Carlo QM simulation (p-pulse, delay, then
measure)
probability P1
A260 um2 (Nc1.7)
A2500 um2 (Nc5.3)
time (ns)
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State Decay vs. Junction Area
Monte-Carlo QM simulation (p-pulse, delay, then
measure)
Nc2/2
A18 mm2 (Nc0.45)
probability P1
A260 mm2 (Nc1.7)
A2500 mm2 (Nc5.3)
time (ns)
Need Nc lt 0.3 (A lt 10 mm2) to statistically avoid
resonances


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State Measurement and Junction Resonances
Number resonances swept through
1
tp
Couple to more resonances
0
qubit
junction resonances
Nc gtgt 1, Landau-Zener tunneling
(10 ns)-1
With tp 10 ns, explains fidelity loss in
measurement!