This project is an analytical study of quantum error correction and quantum control. The aim is to develop theoretical and computational techniques to construct error correction codes for quantum channels with general noise, based on matrix- and Lie-theoretic considerations.
Quantum computing is a rapidly-growing area of multidisciplinary research. If large-scale quantum computers can be built, they will be able to solve important problems that lie beyond the capabilities of current classical computers. While the development of quantum computers promises far-reaching implications, there are still many open theoretical questions and experimental challenges that must be overcome. For example, a quantum computer must employ a method to correct data errors that result from the inevitable uncontrollable interaction between a quantum system and its environment, a phenomenon known as decoherence. One of the main goals of this project is to further develop algorithms for error correction in a quantum channel. The project will also investigate other mathematical problems in quantum control theory.
