Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates

Understand

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation.

• Automorphism of gauge group naturally gives global symmetries of gauge theories.
• In this work we study such symmetries in gauge theories induced by automorphisms of the gauge group, when the gauge theories have nontrivial topological actions in different spacetime dimensions.
• We discover the automorphism symmetry can be extended, become a higher group symmetry, and/or become a non-invertible symmetry.