Towards optimized dynamical error control and algorithms for quantum information processing
Wan-Jung Kuo · ProQuest Demo Repository · 2012
Two topics in the field of quantum information processing, optimized dynamical error suppression and quantum algorithms, are considered here. ? The computational errors induced by the surrounding environment is one of the main obstacles in building a quantum computer. Engineering powerful techniques to combat errors in quantum devices is highly demanding. In the first part of this thesis, I focus on one quantum error correction technique, dynamical decoupling (DD), introduced in Chapter 1. Chapter 2 is dedicated to nested UDD (NUDD), a highly efficient decoupling scheme that utilizes the decoupling characteristics of UDD by multi-layer nesting. UDD (1-layer NUDD) is an optimal DD method for eliminating single-qubit general dephasing, and QDD (2-layer NUDD) is a near-optimal DD method for eliminating one qubit general decoherence. I present a rigorous analytical proof of the performance and universality of QDD/NUDD, and obtain an explicit formula for the decoupling order of each error type, which elucidates the relationship between the error type and characteristics of NUDD. From the explicit formula, a NUDD scheme can be designed accordingly such that optimal efficiency of NUDD is achieved. Moreover, the highly efficient error cancellation mechanism is revealed by the analysis. The proof of QDD has been published in [31], and the proof of NUDD will be submitted for publication shortly. ? Chapter 3 is devoted to the Adiabatic Quantum Computation (AQC). In this work (published in [44]), a general time-optimal strategy, which in principle can optimize any quantum adiabatic algorithm for which the gap is known or can be estimated, is formulated. In addition, I present a natural differential-geometric framework for AQC.