Mathematics Colloquium
Eric Kubischta
University of Maryland
Title: Quantum Codes From Symmetry
Date: Monday, February 3, 2025
Place and Time: Love 101, 3:05-3:55 pm
Abstract. Quantum computers are inherently subject to noise, necessitating fault-tolerant quantum error-correcting codes to achieve quantum advantage. This requires performing logical operations indirectly, through physical operations that preserve the codespace. While generic physical operations are not fault-tolerant, transversal gates, which act locally on individual qubits, are intrinsically fault-tolerant, making them particularly appealing for practical implementation. The set of logical operations achievable with transversal gates forms a finite group G that is an invariant of equivalent quantum codes. In this talk, I will present my recent contributions to a novel top-down approach to quantum error correction, where quantum codes are systematically derived from the group G. Using tools from the representation theory of finite and unitary groups, I will show how the structure of G informs the construction of quantum codes and governs their error-correcting properties. This perspective not only reveals novel quantum codes but also highlights deep connections between representation theory and the foundations of quantum error correction.