Prime number factorization using a spinor Bose-Einstein condensate inspired topological quantum computer

TL;DR

This paper explores using a spinor Bose-Einstein condensate-based topological quantum computer to implement Shor's factorization algorithm, analyzing its excitation spectrum, fusion rules, and gate design, with considerations of decoherence effects.

Contribution

It introduces a novel topological quantum computing platform based on the quantum double $\\mathcal{D}(Q_8)$ anyon model, including circuit architecture and noise analysis.

Findings

All but one quantum gate can be exactly compiled

The model's computational potential is comparable to Majorana-based systems

Decoherence effects are modeled and analyzed

Abstract

Inspired by non-abelian vortex anyons in spinor Bose-Einstein condensates, we consider the quantum double $\mathcal{D}(Q_8)$ anyon model as a platform to carry out a particular instance of Shor's factorization algorithm. We provide the excitation spectrum, the fusion rules, and the braid group representation for this model, and design a circuit architecture that facilitates the computation. All necessary quantum gates, less one, can be compiled exactly for this hybrid topological quantum computer, and to achieve universality the last operation can be implemented in a non-topological fashion. To analyse the effect of decoherence on the computation, a noise model based on stochastic unitary rotations is considered. The computational potential of this quantum double anyon model is similar to that of the Majorana fermion based Ising anyon model, offering a complementary future platform for topological quantum computation.