Abstract:

Quantum computation (QC) holds the promise of efficiently solving problems which are practically intractable for classical computers. However, realizing this advantage requires the precise control of a quantum information processor (QIP) and effective protection of this processor from the pernicious inuence of decoherence induced by the surrounding environment. Therefore, the ability to generate high-fidelity logical operations in the presence of environmental coupling is crucial.

Methods of optimal control are applied to the field of quantum information processing, providing practical solutions for the generation of logical operations and the suppression of undesired environmental effects. The work contained in this dissertation explores important aspects of system and control design. Results obtained in this work (i)?illustrate how practical QC can be greatly facilitated by optimal control theory and (ii)?reveal interesting physical insights through the discovery of effective control mechanisms.

A special design of the physical structure of quantum information systems is formulated which is naturally immune to certain types of decoherence and yields tremendous flexibility in the construction of logical operations for QC. A fundamental component of this design involves encoding the logical basis states of a quantum bit into multiple physical levels of the corresponding quantum system. This design also makes the QIP better suited for the interaction with ultrafast broadband laser fields used in quantum control applications. Numerical simulations demonstrate the utility of this encoding approach for thermally excited quantum systems.

Optimization algorithms are developed which generate controls that protect the QIP from the effects of the environment, with or without the weak-coupling or Born approximation, and simultaneously achieve a target objective, e.g., a state-to-state transition or unitary quantum operation. For the optimal control of quantum operations, a novel state-independent distance measure is developed to evaluate operation fidelity. For the state control of open quantum systems, an accurate and straightforward numerical propagation routine is derived in the framework of the Born approximation. The resulting optimal controls cleverly identify and use various properties of the composite system to effectively attain the desired objectives. The optimal controls obtained for systems with reversible dynamics utilize induced coherence revivals and are robust to random variations in system-environment coupling strengths. For irreversible dynamics of the Born approximation, the optimal controls employ decoherence-free states and are practically insensitive to the structure of random environments.