Systematic distillation of composite Fibonacci anyons using one mobile quasiparticle

TL;DR

This paper demonstrates how to perform universal quantum computation with Fibonacci anyons using only one mobile quasiparticle and a limited set of measurements, by systematically constructing braid sequences for initialization.

Contribution

It introduces a systematic method to initialize composite Fibonacci anyons with high accuracy using braid sequences based on a quantum search algorithm, reducing the need for extensive braiding or measurements.

Findings

Universal quantum computation is achievable with limited quasiparticle mobility.

A new systematic construction of braid sequences for initialization is provided.

The method avoids the Solovay-Kitaev theorem by using a quantum search algorithm.

Abstract

A topological quantum computer should allow intrinsically fault-tolerant quantum computation, but there remains uncertainty about how such a computer can be implemented. It is known that topological quantum computation can be implemented with limited quasiparticle braiding capabilities, in fact using only a single mobile quasiparticle, if the system can be properly initialized by measurements. It is also known that measurements alone suffice without any braiding, provided that the measurement devices can be dynamically created and modified. We study a model in which both measurement and braiding capabilities are limited. Given the ability to pull nontrivial Fibonacci anyon pairs from the vacuum with a certain success probability, we show how to simulate universal quantum computation by braiding one quasiparticle and with only one measurement, to read out the result. The difficulty lies in initializing the system. We give a systematic construction of a family of braid sequences that initialize to arbitrary accuracy nontrivial composite anyons. Instead of using the Solovay-Kitaev theorem, the sequences are based on a quantum algorithm for convergent search.