Minimal Quantum Circuits for Simulating Fibonacci Anyons

arXiv (Cornell University)

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.

Authors 5

1. Sary Bseiso

   University of Illinois Urbana-Champaign

   Affiliation as printed

   Department of Physics , University of Illinois at Urbana-Champaign , 1110 West Green Street , Urbana , IL 61801 , USA

2. Joel C. Pommerening Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information , RWTH Aachen University , D-52056 Aachen , Germany

3. Richard R. Allen

   Massachusetts Institute of Technology

   Affiliation as printed

   Center for Theoretical Physics , Massachusetts Institute of Technology , Cambridge , MA 02139 , USA

4. Steven H. Simon

   Center for Theoretical Physics

   Affiliation as printed

   Rudolf Peierls Centre for Theoretical Physics , Parks Road , Oxford , OX1 3PU , UK

5. Layla Hormozi

   Brookhaven National Laboratory

   Affiliation as printed

   Computational Science Initiative , Brookhaven National Laboratory , Upton , NY 11973 , USA