quantum firmware

QuantumFirmware: Engineeringerrorresistanceatthe - PowerPoint PPT Presentation

QuantumFirmware: Engineeringerrorresistanceatthe physicallevelforquantumcomputation Support MichaelJ.Biercuk QuantumControlLaboratory CentreforEngineeredQuantumSystems


  1. Quantum
Firmware:
 Engineering
error
resistance
at
the
 physical
level
for
quantum
computation 
 Support
 Michael
J.
Biercuk
 Quantum
Control
Laboratory
 Centre
for
Engineered
Quantum
Systems
 School
of
Physics,
The
University
of
Sydney 


  2. Outline
 • Motivation
(quickly)

 • Quantum
Firmware
 for
error
suppression
 at
the
physical
level
 • Noise-filtering:
An
 Experiment-Friendly
 analytical
approach
 • Experiments
–
quantum
firmware
in
the
lab
 • Noise
filtering
in
nontrivial
gates


  3. Decoherence
due
to
environmental
noise:
 A
Fundamental
Limit
 Dephasing 
 Relaxation 


  4. How
do
we
deal
with
this
error?
 • Closed-loop
feedback
control
 
 ⇒ 
Quantum
Error
Correction
 • Open-loop
control
 
 ⇒ Dynamical
Error
Suppression
 Aim:
Improve
QEC
performance
by
driving
 down
physical
error
rates 


  5. Spin
Echo
to
Dynamical
Decoupling
 Hahn
1950,
NMR
 Simple
application
of
control
pulses
suppresses
errors…
 Significant
flexibility
in
pulse
number,
pulse
timing,
pulse
types…
 The
art
is
in
efficient
 sequencing 
 95,
180501
(2005). 

 PRA
58 58,
2733
(1998).

PRA
59, 59,
4178
(1999).

PRL
95

  6. Vision:
 “Quantum
Firmware”
 • Efficient
physical-layer
error
evasion
strategy
 • Simple
implementation
 • Absorbed
into
machine-language
 abstraction:
invisible
to
programmer
 • Useful
for
*any*
quantum
technology
 • Similar
to
DRAM
refreshes


  7. What
are
our
interests:
 • Making
dynamical
error
suppression
accessible
 – i.e.
Please
don’t
speak
group
theory
to
me
 • Calculating
error
rates
in
real
environments
 instead
of
assuming
some
 p
 • Considering
realistic
constraints
imposed
by
 hardware
 • Designing
quantum
control
approaches
 compatible
with
these
constraints



  8. Noise
Filtering


  9. Calculating
the
effect
of
fluctuating
noise
 β (t)
 represents
dephasing
noise
 is
the
error
 Net
Phase
is
convolution
of
noise
and
toggling
frame


  10. Capturing
the
average
behavior
 Time
Domain
Convolution
  
Fourier
Domain
Product
 Uhrig Uhrig
 et
al. et
al. ,
 ,
 PRL
 PRL
 98,
100504
(2007);
 98,
100504
(2007);
Cywinski Cywinski
et
al.,
 
et
al.,
 PRB
 PRB
 77,
174509
(2008).
 77,
174509
(2008).
 Biercuk
 Biercuk
 et
al et
al .,
 .,
 Nature Nature 
458,
996
(2009).

Biercuk
et
al.,
 ,
996
(2009).

Biercuk
et
al.,
 J.
Phys.
B J.
Phys.
B 
44,
154002
(2011).
 ,
154002
(2011).


  11. Capturing
the
average
behavior
 Time
Domain
Convolution
  
Fourier
Domain
Product
 Coherence: Coherence
preserved
if
 F 
small
for
dominant
 frequencies
 Uhrig Uhrig
 et
al. et
al. ,
 ,
 PRL
 PRL
 98,
100504
(2007);
 98,
100504
(2007);
Cywinski Cywinski
et
al.,
 
et
al.,
 PRB
 PRB
 77,
174509
(2008).
 77,
174509
(2008).
 Biercuk
 Biercuk
 et
al et
al .,
 .,
 Nature Nature 
458,
996
(2009).

Biercuk
et
al.,
 ,
996
(2009).

Biercuk
et
al.,
 J.
Phys.
B J.
Phys.
B 
44,
154002
(2011).
 ,
154002
(2011).


  12. Fully
characterize
any
sequence
by
F
 Stopband 
 Passband 
 Rolloff
~ 
 Filter
Order 
 Filter Function Normalized Frequency [ �� ] Biercuk
et
al.,
 Biercuk
et
al.,
 J.
Phys.
B J.
Phys.
B 
44,
154002
(2011).
 ,
154002
(2011).


  13. Fully
characterize
any
sequence
by
F
 Plug-In High Pass Filter PHP-1000+ Typical Performance Curves Insertion Loss 0 10 20 30 Insertion Loss (dB) 40 50 60 70 80 90 100 1 10 100 1000 10000 Frequency (MHz) Biercuk
et
al.,
 Biercuk
et
al.,
 J.
Phys.
B J.
Phys.
B 
44,
154002
(2011).
 ,
154002
(2011).


  14. Timing
Constraints
Reduce
Performance
 (Daniel
didn’t
tell
the
whole
story…there
are
other
prices
to
pay)
 Filter Function Dimensionless Angular Frequency ( 2 � Hz � ) 10
GHz
clocking
in
1
ms
experiment
 reduces
performance
by
80
dB
@
 ωτ = 1

 Biercuk,
Doherty,
Uys ,
J.
Phys.
B
 44 44,
154002
(2011).


  15. Digital
 modulation
for
large
systems
 The
Walsh
Functions
 Walsh Index, n Time Bin Normalized Pulse Location Other
benefits:
ease
of
sequencing,
unified
framework,
long-time
storage…
 For
more
see
K.
Khodjasteh’s
talk,
Thursday
2:40
PM 
 Hayes,
Khodjasteh,
Viola,
Biercuk,
 arXiv:
1109.6002,
to
appear
in
PRA


  16. Quantum
Firmware
and
Noise
 Filtering
in
the
lab


  17. Experimental
Quantum
System
 Crystal
of
Beryllium
ions


  18. Ions
in
a
Penning
Trap
 B=4.5
T
 B=4.5
T
 9 Be + 
at
4.5T
 Fluorescence
 Cooling
 Field
Sensitive
 9 Be + 
 F=1
 124
GHz
 F=2
 ν c ~ 7.6
MHz 7.6
MHz ν z ~ 600
kHz
 600
kHz
 20
kHz ν m ~ 20
kHz 458,
996
(2009).
Biercuk
 et
al .,
 Quant.
Info.
Comp .
9,
920
(2009). 

 Biercuk
 et
al ,.
 Nature 
458

  19. DD
suppresses
decoherence
 1.0 T 2 ~2.5
ms 
 0.8 Population !"# ! 0.6 0.4 0.2 0.0 0 1 2 3 4 Ramsey Precession Time (ms) Biercuk
 et
al .,
 Quant.
Info.
Comp .
9,
920
(2009). 


  20. DD
suppresses
decoherence
 1.0 Coherence
time
increases
~10X
 (for
10
pulses)
 0.8 Probability !" ! # 0.6 0.4 Free-Induction
 0.2 10-pulse
CPMG
 Decay
 0.0 0 10 20 30 40 50 60 Free-Precession Time (ms) Biercuk
 et
al .,
 Quant.
Info.
Comp .
9,
920
(2009). 


  21. The
filter
function
works!
 2.5 n =4 ! 2.0 Error
Probability
 n =5 ! 1.5 n =6 ! 1.0 n =8 ! 0.5 n =10 ! 0.0 10 20 30 40 50 Total Free Precession Time (ms) Solid:
CPMG,
Open:
UDD
(Different
Pulse
Spacings) 
 Biercuk
 et
al .,
 Nature 
458 458,
996
(2009).
Biercuk
 et
al .,
 Phys.
Rev.
A 
79 79
062324
(2009).


  22. The
filter
function
works!
 2.5 n =4 ! 2.0 Error
Probability
 n =5 ! 1.5 n =6 ! 1.0 n =8 ! 0.5 n =10 ! 0.0 10 20 30 40 50 Total Free Precession Time (ms) Solid:
CPMG,
Open:
UDD
(Different
Pulse
Spacings) 
 Biercuk
 et
al .,
 Nature 
458 458,
996
(2009).
Biercuk
 et
al .,
 Phys.
Rev.
A 
79 79
062324
(2009).


  23. Noise
Injection:
Modeling
Other
Qubits
 5 10 4 10 3 10 1/ ω 
 2 10 1 10 0 10 -1 10 -2 10 -3 10 6 8 2 4 6 8 2 4 6 8 2 3 4 10 10 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 6 8 2 4 6 8 2 4 6 8 2 3 4 10 10 10 ! (2 " Hz) 79
062324
(2009). 
 Biercuk
 et
al .,
 Nature 
458,
996
(2009).
Biercuk
 et
al .,
 Phys.
Rev.
A 
79

  24. UDD
can
outperform
CPMG
 Red=UDD,
Black=CPMG
 UDD
 Better
 2.5 V N = 0.9 V 2.0 Noise
Strength
 Error
Probability
 Error Probability 0.7 V 1.5 0.5 V 1.0 0.3 V 0.5 CPMG
 Better
 0.1 V 0.0 0 1 2 3 4 Free Precession Time (ms) S � ( � ) (rad/s) 4 10 1 10 -2 10 (c) -5 10 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 2 3 4 10 10 10 Angular Frequency (rad/s) MJB
 et
al .,
 Nature 
458 458,
996
(2009).
MJB
 et
al .,
 Phys.
Rev.
A 
79 79
062324
(2009).,
MJB
et
al
QIC
9,
920
(2009)


  25. Optimization
by
autonomous
feedback
 1 CPMG 4 UDD 2 Error Probability LODD 0.1 4 2 0.01 5X
improvement
over
UDD
 4 8X
improvement
over
CPMG
 2 0.001 1 2 3 4 Total Free Precession Time (ms) We
have
realized
improved
performance
by
tailoring
the
filter
function 
 Biercuk
 et
al .,
 Nature 
458 458,
996
(2009)


  26. Interlude:
Mike’s
opinion
on
UDD


  27. Dynamical
decoupling
studies
w/ions…


  28. Why
did
this
work?
High-fidelity
control.
 99.92%
Fidelity/Gate
 1.00 0.95 Average Fidelity 0.90 1 0.85 0.80 0 ! " =185 ! s 0.5 1.0 1.5 2.0 Pulse Length (ms) 0.75 50 100 150 200 Computational Gate Number Need
to
develop
new
 Need
to
develop
new
 flexible flexible 
high-fidelity
 
high-fidelity
 control
hardware,
and
understand
gate
errors control
hardware,
and
understand
gate
errors 
 77,
012307
(2008). 
 Biercuk
 et
al .,
 Quant.
Info.
Comp .
9,
920
(2009). 
 PRL
 97 97 ,
 220407 
 (2006). 
PRA 
77

  29. Dynamical
protection
beyond
Memory
 Green,
Uys,
&
Biercuk,
 arXiv:1110.6686


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