In quantum computing and quantum communication, information is stored in the states of quantum mechanical systems. A major obstacle to quantum information processing is that one has to combat a high level of noise affecting these states. Consequently, scalable quantum computer architectures require mechanisms that ensure fault-tolerance of operations. The design is complicated by the fact that the corrective steps themselves can be faulty. As a result, the predominant computational steps in such architectures are concerned with quantum error-correction (for example, syndrome calculations, error location and correction) and with encoded operations acting on the code space.
The goal of this project is to extend the theory of quantum error-correcting codes and related areas. Specifically, the topics being explored in this project include (i) families of stabilizer codes that are well suited for fault-tolerant quantum computing; (ii) the theory of operator quantum error-correcting codes (a recent generalization of various active and passive quantum error-control methods); (iii) stabilizer codes over finite rings; and (iv) quantum-assisted network coding.
