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Using Randomness for Coherent Quantum Control

Randomization may be more advantageous when i) large control groups/ long time intervals and/or ii) rapidly fluctuating interactions. Viola & Knill, PRL 94 , 060502 (2005). Single qubit : decoherence suppression

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Using Randomness for Coherent Quantum Control

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  1. Randomization may be more advantageous when i) large control groups/ long time intervals and/or ii) rapidly fluctuating interactions Viola & Knill, PRL 94, 060502 (2005) • Single qubit: decoherence suppression • Identify situations where a random protocol is more suitable • combining protocols leads to a better performance Santos & Viola, forthcoming 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. Interaction picture: Decoherence function in the absence of control, Ohmic bath: system-bath interaction strength High T Low T bath temperature bath correlation time Decoherence from a Quantum Bosonic Environment Model is exactly solvable

  3. Goal: Average out the interaction with the environment Bang-Bang: Arbitrarily strong and instantaneous control operations drawn from a group Sequences of bang-bang operations + free evolutionsDecoupling if + - Low T Cyclic dynamical scheme: High T Deterministic Dynamical Decoupling Viola & Lloyd, PRA 94, 060502 (1998) Viola et al, PRL 82, 2417 (1999)

  4. pulse Naïverandom protocol: at (PAREC method) Hybrid protocol:combines deterministic and random protocols (embeds a deterministic scheme into a stochastic one) Acyclic. Toggling/logical frame – evolution follows the applied control Random Dynamical Decoupling

  5. * * High T Low T + + deterministic hybrid no control random 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

  6. * * High T deterministic no control random Time-Dependent Coupling Random pulses may be safer

  7. 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

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