Status of Robust Gate Design by Optimal Control

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Status of Robust Gate Design by Optimal Control

• Janus Halleløv Wesenberg
• University of Aarhus

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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

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Sample-Based Approach

• Now Just minimize J(u)!
• Method optimal control theory

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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

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Performance for Central Ions
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Problem Far-Detuned Ions
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Performance for Far-Detuned Ions

• Includes decay,

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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

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Magnus Expansion

• Second order Magnus expansion allows us to
  estimate effect on far-detuned ions

H(1) given by the autocorrelation function
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Works for unoptimized fields
Red marks 2nd order Magnus estimate
Field
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but optimization tricks Magnus
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More Iterations are Even Worse
Niter1100
Niter450
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Source of Spread
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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

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Magnus Working
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Resulting Field
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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

To be published
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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

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Entangling Power
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Magnus-based Sampling

• Seems very promising

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Instance Selection
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Unitary Instance Selection
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Bus Architecture
Fully interconnected
Bus

• Interaction strengths up to GHz at typical ion
  distances.

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Calculating dJ/du

• For a general dynamical system,
• We consider the objective functional

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OCT overview