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Status of Robust Gate Design by Optimal Control

Status of Robust Gate Design by Optimal Control. Janus Hallel øv Wesenberg University of Aarhus. 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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Status of Robust Gate Design by Optimal Control

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  1. Status of Robust Gate Design by Optimal Control Janus Halleløv Wesenberg University of Aarhus

  2. 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

  3. Sample-Based Approach Instance parameters Objective functional Field parameters Performance index • Now: Just minimize J(u)! • Method: optimal control theory ESQUIRE Meeting, Lund, January 2005

  4. 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

  5. Performance for Central Ions

  6. Problem: Far-Detuned Ions ESQUIRE Meeting, Lund, January 2005

  7. Performance for Far-Detuned Ions • Includes decay, ESQUIRE Meeting, Lund, January 2005

  8. 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

  9. Magnus Expansion • Second order Magnus expansion allows us to estimate effect on far-detuned ions: H(1) given by the autocorrelation function ESQUIRE Meeting, Lund, January 2005

  10. Works for unoptimized fields Red marks: 2nd order Magnus estimate Field ESQUIRE Meeting, Lund, January 2005

  11. … but optimization tricks Magnus ESQUIRE Meeting, Lund, January 2005

  12. More Iterations are Even Worse Niter=1100 Niter=450 ESQUIRE Meeting, Lund, January 2005

  13. Source of Spread ESQUIRE Meeting, Lund, January 2005

  14. 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

  15. Magnus Working ESQUIRE Meeting, Lund, January 2005

  16. Resulting Field ESQUIRE Meeting, Lund, January 2005

  17. Entangling Power Decay Decay • 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] ESQUIRE Meeting, Lund, January 2005

  18. 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

  19. Entangling Power ESQUIRE Meeting, Lund, January 2005

  20. Magnus-based Sampling • Seems very promising ESQUIRE Meeting, Lund, January 2005

  21. Instance Selection ESQUIRE Meeting, Lund, January 2005

  22. Unitary Instance Selection ESQUIRE Meeting, Lund, January 2005

  23. Bus Architecture • Interaction strengths: up to GHz at typical ion distances. Fully interconnected Bus ESQUIRE Meeting, Lund, January 2005

  24. Calculating dJ/du E.g. Schrödinger equation ”Penalty function” • For a general dynamical system, • We consider the objective functional ESQUIRE Meeting, Lund, January 2005

  25. OCT overview ESQUIRE Meeting, Lund, January 2005

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