Collaborative Research: Mathematical Aspects of Quantum Information Science

Iowa State University, Ames IA

Investigators

Abstract

This project studies mathematical problems arising in quantum information science. The aim is to develop theoretical and computational techniques to solve problems concerning the development of scalable quantum computers. The investigators will (1) use the theory of completely positive linear maps to study the criteria for the existence of quantum operations connecting prescribed quantum states and to provide construction schemes for associated quantum operations; (2) use generalized numerical ranges to study the theory and implementation of quantum error correction codes; and (3) use optimization techniques based on Lie theory to study the best approximation of quantum states to improve quantum control theory. The project will involve collaborations between theorists and experimentalists so that experiments can be conducted to test the theory and conjectures as well as to provide insights for theoretical development. 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. This project aims to further develop the theory and algorithms for error correction in a quantum channel and to investigate the construction of quantum operations connecting prescribed quantum states. The project will also investigate mathematical problems in quantum control theory such as approximating a desired quantum state by more accessible ones.