Related papers: Topological quantum computing
Non-Abelian states of matter, in which the final state depends on the order of the interchanges of two quasiparticles, can encode information immune from environmental noise with the potential to provide a robust platform for topological…
Majorana bound states have been a focus of condensed matter research for their potential applications in topological quantum computation. Here we utilize two charge-qubit arrays to explicitly simulate a DIII class one-dimensional…
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators…
Majorana bound states are quasiparticle excitations localized at the boundaries of a topologically nontrivial superconductor. They are zero-energy, charge-neutral, particle-hole symmetric, and spatially-separated end modes which are…
Over the last decade, there have been considerable efforts to observe non-abelian quasi-particles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasi-particles beyond…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
The topological classification of energy bands has laid the groundwork for the discovery of various topological phases of matter in recent decades. While this classification has traditionally focused on real-energy bands, recent studies…
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…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
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…
We analyze the evidence of Majorana zero modes in nanowires that came from tunneling spectroscopy and other experiments, and scout the path to topologically protected states that are of interest for quantum computing. We illustrate the…
The possibility of quantum computation using non-Abelian anyons has been considered for over a decade. However the question of how to obtain and process information about what errors have occurred in order to negate their effects has not…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
Executing quantum algorithms using Majorana zero modes - a major milestone for the field of topological quantum computing - requires a platform that can be scaled to large quantum registers, can be controlled in real time and space, and a…
Topological excitations are prominent candidates for explaining nonperturbative effects in QCD like confinement. In these lectures, I cover both formal treatments and applications of topological objects. The typical phenomena like BPS…
These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation,…
The idea of topological quantum computation (TQC) is to store and manipulate quantum information in an intrinsically fault-tolerant manner by utilizing the physics of topologically ordered phases of matter. Currently, one of the most…
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes…
The model of a topological quantum computer is a promising one due to its natural resistance to noise and other errors. Operations in such a computer are implemented by braiding the trajectories of anyons. While it is easy to understand how…
Read-Rezayi fractional quantum Hall states are among the prime candidates for realizing non-Abelian anyons which in principle can be used for topological quantum computation. We present a prescription for efficiently finding braids which…