High-Fidelity Measurements of Josephson Phase Qubits

1
High-Fidelity Measurements of Josephson Phase
Qubits
UC Santa Barbara
Collaboration with NIST Boulder
John Martinis Andrew Cleland Robert
McDermott Matthias Steffen (Ken Cooper) Eva
Weig Nadav Katz
Markus Ansmann Matthew Neeley Radek Bialczak Erik
Lucero
GS
PD
UCR A. Korotkov UCI C. Yu

• Quantum Integrated Circuit scalable
• Breakthrough in fidelity
• single-shot tomography
• partial measurement
• Tunable qubit easy to use

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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
3
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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IC Fabrication
Qubit
X,Y
readout
Is
Imwave
Z
100mm
(old design)
If
via
junction
Al junction process optical lithography
Al
Al
SiNx
Al
Al2O3 substrate
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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
30dB
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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

9
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?
Theory A. Korotkov, UCR

• Look inside
• wavefunction projection
• First POVM
• in solid state

0?1?
Prob. 1-p/2
State tunneled
Prob. p/2
state preparation
partial measure p
tomography final measure
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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)

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

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Coupled Qubits i-SWAP gate
p
PAB
tosc
A
B
S
1 1
Probability PAB
0 1
1 0
p
tosc
0 0
tosc
i-SWAP gate
i-SWAP
A
CNOT gate with Tomography
B
Turn interaction on/off with bias current
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Future Prospects

• Coherence
• T1 gt 500 ns in progress, need to lengthen Tf
• Breakthrough decoherence from dielectric loss
• STOP USING BAD MATERIALS!
• Demonstrated improvements with new materials
• Single Qubit operations work well
• Tomography, partial measurement demonstrated
• Coupled qubit experiment in DR
• Simultaneous state measurement demonstrated
• Violate Bells inequality soon
• Tunable qubit 4 types of CNOT gates possible
• Scale-up infrastructure (for phase qubits)
• Large C gives long-distance coupling
• Optical Lithography directly scalable
• Large qubits - wiring straightforward
• Wiring 7 qubits/run tested, 100 possible in DR
• Electronics working, scalable

Very optimistic about 10 qubit quantum computer
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Qubit operation Measurement Readout
Reset
time
If
Qubit Cycle
If
U(d)
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Qubit operation Measurement Readout
Reset
Qubit Op Meas Amp
time
If
Qubit Cycle
If
U(d)

fast decay
2000 states
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Qubit operation Measurement Readout
Reset
Qubit Op Meas Amp
time
If
Qubit Cycle
If
U(d)
0

fast decay
2000 states
1
1 F0
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Qubit operation Measurement Readout
Reset
Qubit Op Meas Amp
time
If
Qubit Cycle
If
Measure p1
Is
U(d)
Is
0

fast decay
2000 states
1
1 F0
Switching current
10 mA
SQUID flux
0
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Coupled Qubits Spectroscopy
Cc
A
B
A
C
Cc
1 1
Off Resonant
0 1
1 0
B
0 0
B qubit unbiased
A qubit unbiased
wA/2p (GHz)
wB/2p (GHz)
Flux Bias A
Flux Bias B
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Coupled Qubits Spectroscopy
Cc
A
B
A
C
Cc
1 1
Resonant
0 1
1 0
B
0 0
Moves with bias on B
A qubit unbiased
B qubit biased
wB/2p (GHz)
wA/2p (GHz)
S 74 MHz
Flux Bias B
Flux Bias A
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Coupled Qubits i-swap gate (in time domain)
PAB
p
tosc
A
B
1 1
S
0 1
1 0
Probability PAB
p
tosc
0 0
Magnitude consistent with single qubit fidelity,
mw drive xtalk
tosc
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Cross Coupling when Measurement is Delayed
Qubit gate easy to make, During measurement
coupling still on ! Measurement of 1 state
dissipates energy
Fixed Coupling
p
p
p
A
B
P01 same
P10 same
P10
P01
P11
P11
When measure 1 state pumps energy into 2nd
qubit, producing 0 -gt 1 transition
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I(t)Cx dV/dt
theory
V(t)
Time Scale of Measurement Crosstalk
experiment
V(t)
1
0
16 GHz
I(t)
on resonance
Small crosstalk for misalignment lt1 ns
E/E10
t ns
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Next Project CNOT gate with tomography
i-swap experiment
CNOT ( swap) gate
p
A
A
B
B
meas.
iswap
pulse
X
0
0
Change pulse to vary initial state
Change pulse to vary measurement basis
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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!
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Infrastructure Cryogenics
Installed, working by 2/05 Redesign pot,
precooler/shields New (dense) wiring
design Microwave Nb, CuNi coax

• Dilution Refrigerator for QC
• lt20 mK base temp.
• 10-100x wiring area
• Shielding
• (Fast cooldown, 16 hr)
• (Low operation cost, 6 l/d)
• Wiring for 100 qubits

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Infrastructure Electronics
D/A Converter
Microwave
Control PC
FPGA Sequencer
100Mbit Ethernet
200MHz64bit bus,400KHzI2C bus
SMAcables
Software more difficult
N/A
Hardware modifications more difficult
Example Spin Lock
0
20
40
time (ns)
p/2, 0
p/2, 0
p, 90