Status of Robust Gate Design by Optimal Control Janus Halleløv Wesenberg University of Aarhus.
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Status of Robust Gate Design by Optimal Control Janus Halleløv Wesenberg University of Aarhus
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Transcript of Status of Robust Gate Design by Optimal Control Janus Halleløv Wesenberg University of Aarhus.
Status of Robust Gate Design by Optimal Control
Janus Halleløv WesenbergUniversity of Aarhus
ESQUIRE Meeting, Lund, January 2005
Talk Outline
• Robust gate design by optimal control.
• Problems of sample-based approach• Magnus expansion allows area-
samples• Performance with area-samples• Summary and outlook
ESQUIRE Meeting, Lund, January 2005
Sample-Based Approach
• Now: Just minimize J(u)!– Method: optimal control theory
Field parameters Objective functional
Instance parameters
Performance index
ESQUIRE Meeting, Lund, January 2005
Talk Outline
• Robust gate design by optimal control.
• Problems of sample-based approach• Magnus expansion allows area-
samples• Performance with area-samples• Summary and outlook
Performance for Central Ions
ESQUIRE Meeting, Lund, January 2005
Problem: Far-Detuned Ions
ESQUIRE Meeting, Lund, January 2005
Performance for Far-Detuned Ions
• Includes decay,
ESQUIRE Meeting, Lund, January 2005
Talk Outline
• Robust gate design by optimal control.
• Problems of sample-based approach• Magnus expansion allows area-
samples• Performance with area-samples• Summary and outlook
ESQUIRE Meeting, Lund, January 2005
• Second order Magnus expansion allows us to estimate effect on far-detuned ions:
Magnus Expansion
H(1) given by the autocorrelation function
ESQUIRE Meeting, Lund, January 2005
Works for unoptimized fields
2 4 6 8 1010
-5
10-4
10-3
10-2
10-1
100
/0
1-F
0 2.5 5 7.5 10
0
0.25
0.5
0.75
1
||/
0
0 2.5 5 7.5 10 -2
0
2
4
Arg
()/
2
t 0/
1
2
Red marks: 2nd order Magnus estimate
Field
ESQUIRE Meeting, Lund, January 2005
… but optimization tricks Magnus
0.99
0.990.99
0.990.99
0.99
0.99
0.999
0.9990.999
0.999
0.999 0.999
/0
-0.4 -0.2 0 0.2 0.4
0.8
0.9
1
1.1
1.2
2 4 6 8 1010
-8
10-7
10-6
10-5
10-4
10-3
/0
1-F
ESQUIRE Meeting, Lund, January 2005
More Iterations are Even Worse
2 4 6 8 1010
-8
10-7
10-6
10-5
10-4
10-3
/0
1-F
2 4 6 8 1010
-8
10-7
10-6
10-5
10-4
10-3
/0
1-F
Niter=450
Niter=1100
ESQUIRE Meeting, Lund, January 2005
Source of Spread
2 3 4 5 6 7 8 9 1010
-7
10-6
10-5
10-4
10-3
/0
1-F
ESQUIRE Meeting, Lund, January 2005
Talk Outline
• Robust gate design by optimal control.
• Problems of sample-based approach• Magnus expansion allows area-
samples• Performance with area-samples• Summary and outlook
ESQUIRE Meeting, Lund, January 2005
Magnus Working
0.99
0.99
0.99
0.99
0.99
0.990.99
0.99
0.999
0.999
0.999
0.999
0.9990.999
/0
-0.4 -0.2 0 0.2 0.4
0.8
0.9
1
1.1
1.2
2 4 6 8 1010
-6
10-4
10-2
100
/0
1-F
ESQUIRE Meeting, Lund, January 2005
Resulting Field
0 2.5 5 7.5 10
0
0.25
0.5
0.75
1
||/
0
0 2.5 5 7.5 10-5
0
5
Arg
()/
2
t 0/
1
2
ESQUIRE Meeting, Lund, January 2005
Entangling Power• The excited state is plagued by decay.• Nevertheless, since the entangling power of
the dipole coupling is proportional to the excited state population, we need to populate it.
• Limits obtainable gate fidelity
DecayDecay
[To be published]
ESQUIRE Meeting, Lund, January 2005
Summary and Outlook
• Summary– 2nd order Magnus expansion alone is not
enough to accurately predict performance.
– Together with regular samples, however, the optimization seems to work
• Outlook– We are currently trying to obtain a full
2-qubit gate by optimization
ESQUIRE Meeting, Lund, January 2005
Entangling Power
ESQUIRE Meeting, Lund, January 2005
Magnus-based Sampling
• Seems very promising
ESQUIRE Meeting, Lund, January 2005
Instance Selection
ESQUIRE Meeting, Lund, January 2005
Unitary Instance Selection
ESQUIRE Meeting, Lund, January 2005
Bus Architecture
• Interaction strengths: up to GHz at typical ion distances.
Fully interconnected Bus
ESQUIRE Meeting, Lund, January 2005
Calculating dJ/du
• For a general dynamical system,
• We consider the objective functional
E.g. Schrödinger equation
”Penalty function”
ESQUIRE Meeting, Lund, January 2005
OCT overview
