University of Guelph

Purpose

Quantum error correction (QEC) is a central topic in modern quantum science. At its core, QEC is concerned with protecting encoded quantum information from the errors and noise of quantum systems. Operator quantum error correction (OQEC) and the higher rank numerical range (HRNR) compression formalism combine to provide a unified language where QEC code spaces, subsystems, noise processes, and fault-tolerant symmetries are analyzed as compression problems on Hilbert space. In this framework, the numerical range of an operator and its signature norm allow stabilizer, nonadditive, and subsystem QEC code constructions to be treated on equal footing alongside general, non-Pauli noise models. The goal of the Project is to translate this formalism into a practical toolkit for code discovery and analysis. Simultaneously, the Project will develop AIassisted, data-driven workflows to classify and co-design nonadditive and subsystem codes that are optimized for specific noise environments.