It's the Symmetry, Stupid: Gearing Up Tensor Networks for the Topological Quantum Revolution

Quantum computers currently lose information faster than they can calculate, and this project aims to build the mathematical toolkit to stop that leakage. The problem is that quantum information is fragile—any interaction with the outside world corrupts it. Existing error-correction methods work for simple quantum systems, but they fail for the exotic, topological states of matter that could make quantum computers truly robust. Topological phases store information in the global shape of a quantum system, not in any single particle, making them naturally resistant to local disturbances. But physicists lack the mathematical language to describe and control these states efficiently. This project develops tensor networks—a way of representing complex quantum systems as interconnected grids of simpler pieces—and extends them to handle the non-local, categorical symmetries that topological phases exhibit. If successful, the work will produce a practical computational toolbox for designing quantum error-correcting codes that actually work at scale. It will also clarify the deep relationship between quantum entanglement, error correction, and the holographic principle—a connection that currently sits at the frontier of fundamental physics. This is primarily curiosity-driven fundamental science, but the same kind of mathematical insight that once turned abstract group theory into the backbone of modern particle physics could, here, turn fragile qubits into reliable quantum computers.