Dr. Tyler Ellison
Purdue University
Topological stabilizer models on continuous variables
Location: 1080 Physics Research Building
Faculty Host: Brian Skinner
Abstract: Quantum-error correcting codes are essential to building quantum computers that are reliable in the presence of a noisy environment and faulty operations. One of the most promising classes of quantum-error correcting codes are the topological stabilizer codes. These are exemplified by the toric code, which doubles as one of the simplest models for topological order. In previous work, we have shown that topological stabilizer codes can be constructed for a wide class of Abelian topological orders, so long as they admit an anyon with bosonic exchange statistics. In this talk, I will describe how an even wider class of topological orders, some of which do not have bosonic anyons, can be represented by topological stabilizer models on continuous variable degrees of freedom (i.e., where the state space is that of a harmonic oscillator). This has deep connections to putting Chern-Simons theories on a lattice and produces, to the best of our knowledge, the first examples of controllably-solvable models for certain chiral topological phases of matter.
This work was done in collaboration with Julio Magdalena de la Fuente, Meng Cheng, and Dominic Williamson and is based on arXiv:2411.04993.
Bio: Tyler Ellison's work focuses on problems at the intersection of quantum information and quantum matter. He is especially interested in the development of quantum-error correcting codes inspired by ideas from condensed matter physics. He received his PhD from the University of Washington in 2021, and subsequently did a postdoc at Yale University. He is currently a postdoctoral fellow at Perimeter Institute and will be starting as an assistant professor at Purdue University in the Fall of 2025.
