Quantum Circuits for Simulating Fibonacci AnyonsConfirmed

by Layla Hormozi (Brookhaven National Laboratory)

Wednesday Dec 10, 2025, 11:00 AM → 12:30 PM America/Toronto

PI/4-405 - Bob Room (Perimeter Institute for Theoretical Physics)

The Fibonacci topological order is the prime candidate for the realization of universal topological quantum computation, and when simulated on qubit arrays, has the potential to be an effective quantum error correcting code. Here, we devise quantum circuits to demonstrate the non-Abelian nature of the doubled Fibonacci topological order, as realized in the Levin-Wen string net model. Our circuits effectively initialize the ground state, create excitations, twist and braid them, all in the smallest lattices possible. We further design methods to determine the fusion amplitudes and braiding phases of multiple excitations by carrying out a single qubit measurement. We show that, at the minimal level, the fusion channels of the doubled Fibonacci model can be detected using only three qubits, twisting phases can be measured using five, and braiding can be demonstrated using nine qubits. We then describe how these designs can be generalized for large scale implementations. These designs provide the simplest possible settings for demonstrating the properties of Fibonacci anyons and can be used as realistic blueprints for implementation on many modern quantum architectures. Work is based on arXiv:2407.21761 plus some new results.