Physics – Quantum Physics
Scientific paper
2011-07-21
Physics
Quantum Physics
36 pages, many figures and tables
Scientific paper
Using optimal control theory, we study the optimisation of quantum gates for coupled spin systems, in the presence of Markovian and non-Markovian decoherence. In both models we find that good solutions with small field magnitudes can be efficiently obtained by carrying out multiple trials for any given problem with a well-chosen initial value of the field and a cut-off for the iteration number; still, there are significant differences between both cases. Short gate operation times are desirable in the Markovian case while longer target times can improve gate fidelities in non-Markovian settings via coherence revivals. Even for short gate operation times the mechanisms by which the controls operate differ. For a small number of noise qubits, the gate fidelities can be improved by applying strong fields that shift the system qubits out of resonance with the noise qubits but such fields will not improve fidelities and may be detrimental for Markovian dephasing or relaxation effects. In the Markovian case, we generally find that the optimal fields obtained without considering the environment cannot be improved substantially by taking the environment into account and computation time is saved if the fields are preoptimised neglecting decoherence. On the other hand, taking the environment into account tends to substantially improve fidelities for small non-Markovian reservoirs. However, such improvements are strongly dependent on the noise qubits being shielded from the control. If the control inadvertently affects the dynamics of the noise qubits, high gate fidelities may be impossible to obtain unless both the system and noise qubits are fully controlled.
Floether Frederik
Fouquieres Pierre de
Schirmer Sophie
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