Using Randomness for Coherent Quantum Control

1
Using Randomness for Coherent Quantum Control
Lea F. Santos and Lorenza Viola Department of
Physics and Astronomy Dartmouth College

• Deterministic vs. RANDOM dynamical decoupling

2
Decoherence from a Quantum Bosonic Environment
Model is exactly solvable
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Deterministic Dynamical Decoupling
Viola Lloyd, PRA 94, 060502 (1998) Viola et al,
PRL 82, 2417 (1999)
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Random Dynamical Decoupling
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Deterministic vs. Random Decoupling Numerical
Results
Fixed time interval
i) large number of control pulses all protocols
are equivalent ii) small number of control
pulses hybrid may perform better
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Time-Dependent Coupling
Random pulses may be safer
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Conclusions

• Comparison between deterministic and RANDOM
  dynamical decoupling
• for a single qubit quantum environment

• There are situations where
• 
  combined protocols (deterministic random)
• 
  may perform better (hybrid protocol)
• 
  randomized control is more recommendable
• 
  when the coupling is fast oscillating, for
  example

• Further work is necessary to expand the analysis

• References
• L. Viola and S. Lloyd, PRA 94, 060502 (1998)
• L. Viola, E. Knill and S. Lloyd, PRL 82, 2417
  (1999)
• L. Viola and E. Knill, PRL 94, 060502 (2005)
• O. Kern , G. Alber and D. L. Shepelyansky, Eur.
  Phys. J. D 32, 153 (2005)
• O. Kern and G. Alber, quant-ph/0506038
• L. F. Santos and L. Viola, forthcoming