Quantum control for time-dependent noise

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Kabytayev, Chingiz
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The main obstacles to implementing ideal quantum operations are unwanted interactions of quantum systems with the environment and noise in control fields. This problem can be tackled by methods of quantum control. Among these methods are composite pulse (CP) sequences which have long been employed in nuclear magnetic resonance (NMR) to mitigate the effects of systematic errors in the control. CP sequences have been initially developed to correct for static but otherwise unknown errors in the amplitude or frequency of the driving field. One of the challenges to the systematic incorporation of these control protocols into practical quantum information systems remains the limited understanding of CP performance in the presence of time-dependent noise. Treating the influence of time-dependent noise processes on quantum control operations has been facilitated by recent advances in dynamical error suppression based on open-loop Hamiltonian engineering. These approaches provide a general framework for understanding and mitigating non-Markovian time- dependent noise in a finite-dimensional open quantum system. Particularly, arbitrary single-qubit control characteristics may be captured quantitatively in filter-transfer functions (FF) using methods of spectral overlap in the frequency domain. In this thesis work, we present a systematic study of control pulse sequences in the presence of time-dependent noise. We use a combination of analytic formulations based on FFs and numerical simulations to demonstrate that CPs are able to effectively suppress control errors caused by time-dependent processes possessing realistic noise power spectra. We provide a geometric interpretation of CP performance under time-dependent amplitude noise, further linking the FF formalism with known techniques in CP construction. We also develop new optimized pulse sequences that act as notch filters for time-dependent noise. These high-fidelity control protocols effectively sup- press errors from the noise sources with sharp features in spectral densities and can be used practically on various quantum architectures. We also present our work on simulation of randomized benchmarking protocols and CPs that have been used experimentally by our collaborators to measure gate errors.
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