Quantum Perspectives on the Clifford Group

The Clifford group is the set of unitary transformations which normalize the Pauli group. This group holds unique prominence in quantum computing as the set of operations on a quantum system that can be efficiently simulated on a classical computer. Additionally, Clifford operations completely characterize stabilizer codes, a class of entanglement-based quantum error-correcting codes. In this talk I will demonstrate how an analysis of the Clifford group, using a graph-theoretic framework, provides a lens for examining quantum dynamics, specifically the evolution of properties most interesting to quantum gravity and quantum information.