Dynamical Suppression Of Noise In Quantum Systems

Achieving high fidelity quantum control over quantum system is of vital importance in quantum information processing.Yet various of problems impedes our pursuit towards it.First,the inevitable coupling between the quantum system and the bath leads to the so called decoherence,under which situation the system loses quantumness over time.Second,errors may be incorporated into the control operation,resulting in the evolution deviation from its ideal trajectory.Researchers in the community have both theoretically and experimentally proposed numerous schemes to mitigate the errors in the quantum control procedure,which can be classified into two categories,i.e.the closed-loop quantum control and the open-loop quantum control.The essence of the latter is to modulate the system Hamiltonian with external control field,so as to eliminate the unwanted portion of the Hamiltonian.This technique is measurement-free and do not require the knowledgement of bath information.In this thesis we introduce three research work we have undertaken associating with three important techniques in the open-loop quantum control,i.e.the filter function formalism,dynamical decoupling and the composite pulses.First,dynamical decoupling technique can prolong the existence of quantum coherence.The decoupling sequences can be regarded as a high-pass filter in the frequency domain.We have investigated three complex dynamical decoupling schemes-quadratic dynamical decoupling,periodic dynamical decoupling and concatenated dynamical decoupling-which all contain two kinds of pulses.The three dimensional filter function has been derived in the Bloch sphere picture,enabling us to obtain the decoupling efficacy of arbitrary sequences to the longitudinal relaxation and transverse relaxation.If the total pulse resources is fixed,we indicate that the sequence decoupling performance is the competition of sequence structure effect and the specific pulse number effect.Second,we have validated the decoupling performances of PDD,CDD and QDD in the NMR system and demonstrated the superiority of QDD in experiments for the first time.We propose a method to engineer arbitrary noise environment by modulating the control field.Three-dimensional filter functions are utilized to predict the evolution fidelity decay of DD sequences,presenting perfect consistence with the experiment results.Third,we have studied the robustness of concatenated composite pulses,which are originally proposed to eliminating the static or quasi-static errors,to the time-varying non-markovian errors.Based on the filter function formalism,the suppression capacity difference of concatenated composite pulses to the pulse length error and the off resonance error can be obtained.And we can also find the noise cut frequency threshold where concatenated composite pulses can maintain the robustness to primitive pulses.The experiment data agrees well with filter function prediction.