Related papers: Engineering complex topological memories from simp…
Our understanding of the physics of biological molecules, such as proteins and DNA, is limited because the approximations we usually apply to model inert materials are not in general applicable to soft, chemically inhomogeneous systems. The…
This set of lecture notes forms the basis of a series of lectures delivered at the 48th IFF Spring School 2017 on Topological Matter: Topological Insulators, Skyrmions and Majoranas at Forschungszentrum Juelich, Germany. The first part of…
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the…
We demonstrate how to build a simulation of two dimensional physical theories describing topologically ordered systems whose excitations are in one to one correspondence with irreducible representations of a Hopf algebra, D(G), the quantum…
By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Previous work has shown that a bosonic working medium can yield better performance than a fermionic medium. We expand upon this…
We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations…
The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this…
We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We…
We introduce topological magnetic field in two-dimensional flat space, which admits a solution of scalar monopole that describes the nontrivial topology. In the Chern-Simons gauge field theory of anyons, we interpret the anyons as the…
The Kitaev honeycomb model is a system allowing for experimentally realisable quantum computation with topological protection of quantum information. Practical implementation of quantum information processing typically relies on adiabatic,…
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…
Numerical modelling of quantum effects caused by bosonic or fermionic character of secondaries produced in high energy collisions of different sorts is at the moment still far from being established. In what follows we propose novel…
The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an…
Realizing nonabelian topological orders and their anyon excitations is an esteemed objective. In this work, we propose a novel approach towards this goal: quantum simulating topological orders in the doubled Hilbert space - the space of…
The content of this thesis can be broadly summarised into two categories: first, I constructed modified numerical algorithms based on tensor networks to simulate systems of anyons in low dimensions, and second, I used those methods to study…
Quantum simulation presents itself as one of the biggest advantages of developing quantum computers. Simulating a quantum system classically is almost impossible beyond a certain system size whereas a controllable quantum system inherently…
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not…
The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum…