Abstract: Non-Abelian anyons can non-locally encode quantum information, which can be processed through pair-wise exchanges.
Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decade. However, past two years have seen exciting progress in manifesting and using many-body quantum states with non-Abelian anyons. I will highlight two advancements on superconducting quantum processors my collaborators and I accomplished [1-2]. In the first part, I will discuss theory and experiment on preparing and braiding Ising anyons using graph gauge theory. We braided anyons to realize their statistics. Furthermore we studied the prospect of employing the anyons for quantum computation by creating an entangled state of
anyons encoding three logical qubits. In the second part, I will discuss the efforts to create anyonic states that allow universal quantum computation. Specifically, I will
introduce a scalable dynamical string-net preparation (DSNP) method for realizing Fibonacci string-net condensates (Fib-SNC). This approach enables the creation, braiding, and measurement of Fibonacci anyons in 2D with high accuracy, demonstrating their potential for fault-tolerant universal quantum computation. By sampling the Fib-SNC wavefunction we estimate the chromatic polynomial which is proven to be classically hard. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and to aim at a classically-hard problem.
This seminar will also be viewable on Zoom via https://illinois.zoom.us/my/icmt.seminar?pwd=ZU1KbnBLeXZLUmJKc0oyU205cDNDdz09