Minimal Quantum Circuits for Simulating Fibonacci Anyons

Fuente: arXiv
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Main Authors: Bseiso, Sary, Pommerening, Joel, Allen, Richard R., Simon, Steven H., Hormozi, Layla
Format: Preprint
Published: 2024
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author Bseiso, Sary
Pommerening, Joel
Allen, Richard R.
Simon, Steven H.
Hormozi, Layla
author_facet Bseiso, Sary
Pommerening, Joel
Allen, Richard R.
Simon, Steven H.
Hormozi, Layla
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_21761
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Minimal Quantum Circuits for Simulating Fibonacci Anyons
Bseiso, Sary
Pommerening, Joel
Allen, Richard R.
Simon, Steven H.
Hormozi, Layla
Quantum Physics
Strongly Correlated Electrons
Mathematical Physics
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.
title Minimal Quantum Circuits for Simulating Fibonacci Anyons
topic Quantum Physics
Strongly Correlated Electrons
Mathematical Physics
url https://arxiv.org/abs/2407.21761