Related papers: A Short Introduction to Topological Quantum Comput…
In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models…
Schemes for topological quantum computation are usually based on the assumption that the system is initially prepared in a specific state. In practice, this state preparation is expected to be challenging as it involves non-topological…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons…
Topological quantum computers provide a fault-tolerant method for performing quantum computation. Topological quantum computers manipulate topological defects with exotic exchange statistics called anyons. The simplest anyon model for…
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with…
Topological quantum computation started as a niche area of research aimed at employing particles with exotic statistics, called anyons, for performing quantum computation. Soon it evolved to include a wide variety of disciplines. Advances…
In seminal work (arxiv:quant-ph/9707021) Alexei Kitaev proposed topological quantum computing (arXiv:cond-mat/0010440, arxiv:quant-ph/9707021, arXiv:quant-ph/0001108, arXiv:0707.1889), whereby logic gates of a quantum computer are conducted…
Topological quantum computers promise a fault tolerant means to perform quantum computation. Topological quantum computers use particles with exotic exchange statistics called non-Abelian anyons, and the simplest anyon model which allows…
Quantum computation provides a unique opportunity to explore new regimes of physical systems through the creation of non-trivial quantum states far outside of the classical limit. However, such computation is remarkably sensitive to noise…
In this paper we will present some ideas to use 3D topology for quantum computing extending ideas from a previous paper. Topological quantum computing used \textquotedblleft knotted\textquotedblright{} quantum states of topological phases…
Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault-tolerance that is built-in at the physical level. We show that this topological approach to…
Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
We introduce a pentagon equation solver, available as part of SageMath, and use it to construct braid group representations associated to certain anyon systems. We recall the category-theoretic framework for topological quantum computation…
A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a…
Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can…
We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. These enhanced theories offer more powerful models for quantum computation.…
In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviours. An exciting proposal for…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…
We describe how continuous-variable abelian anyons, created on the surface of a continuous-variable analogue of Kitaev's lattice model can be utilized for quantum computation. In particular, we derive protocols for the implementation of…