Minimal Quantum Circuits for Simulating Fibonacci Anyons

TL;DR

This paper presents minimal quantum circuits that efficiently demonstrate the non-Abelian properties of Fibonacci anyons, including their fusion, braiding, and excitation creation, using the smallest possible qubit systems.

Contribution

It introduces the simplest quantum circuit designs for simulating Fibonacci anyons, enabling practical demonstrations of their topological properties with minimal qubits.

Findings

Fusion channels detectable with 3 qubits

Twisting phases measurable with 5 qubits

Braiding demonstrated with 9 qubits

Abstract

The Fibonacci topological order is the prime candidate for the realization of universal topological quantum computation. We devise minimal 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 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. 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.