Research Projects

Quantum error-correcting codes (QECCs) are vital for mitigating errors inherent in quantum systems due to decoherence and noise. This project explores the generalization of Gottesman-Kitaev-Preskill (GKP) codes using lattice theory within the framework of locally compact abelian groups. We aim to define displacement operators acting on Hilbert spaces L^2(M), construct lattices using these operators, and analyze their logical spaces. This includes determining automorphism groups and their relationship with Clifford operations, enhancing our understanding of fault tolerance in both infinite-dimensional and finite-dimensional quantum systems. By integrating operator algebras and noncommutative geometry, the project seeks to provide foundational advancements in quantum error correction, paving the way for scalable and robust quantum computing technologies.