1. Using Randomness for Coherent Quantum Control
Lea F. Santos and Lorenza Viola
Department of Physics and Astronomy
Dartmouth College
Viola & Knill, PRL 94, (2005)
Randomization may be more advantageous when
i) large control groups/ long time intervals
and/or
ii) rapidly fluctuating interactions
Deterministic vs. RANDOM dynamical decoupling
Santos & Viola, forthcoming
Single qubit: decoherence suppression
Identify situations where a random protocol is more suitable
combining protocols leads to a better performance

2. Decoherence from a Quantum Bosonic Environment
Model is exactly solvable
Interaction picture:
Decoherence function in the absence of control, Ohmic bath:
bath correlation time
system-bath interaction strength
bath temperature
High T
Low T

3. Deterministic Dynamical Decoupling
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 evolutions Decoupling if
High T
Low T + -
Cyclic dynamical scheme:
Viola & Lloyd, PRA 94, (1998)
Viola et al, PRL 82, 2417 (1999)

4. Random Dynamical Decoupling
Naïve random protocol: at
pulse
(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

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

6. Time-Dependent Coupling
High T
* *
deterministic
no control
random
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, (1998)
L. Viola, E. Knill and S. Lloyd, PRL 82, 2417 (1999)
L. Viola and E. Knill, PRL 94, (2005)
O. Kern , G. Alber and D. L. Shepelyansky, Eur. Phys. J. D 32, 153 (2005)
O. Kern and G. Alber, quant-ph/
L. F. Santos and L. Viola, forthcoming