Related papers: Topological phases and quantum computation
These are the lecture notes for a short course on geometric quantization given by the author at the XVIII Modave Summer School on Mathematical Physics, Sep 5 - Sep 9.
We analyze propagation of quantum information along chiral Majorana edge states in two-dimensional topological materials. The use of edge states may facilitate the braiding operation, an important ingredient in topological quantum…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel…
The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a…
This is an introduction to topology of complement to plane curves and hypersurfaces in the projective space and is based on the lectures given in Lumini in February and in ICTP (Trieste) in August of 2005. We discuss key problems concerning…
Two topological phases are equivalent if they are connected by a local unitary transformation. In this sense, classifying topological phases amounts to classifying long-range entanglement patterns. We show that all 2D topological stabilizer…
The Kitaev model is a remarkable spin model with gapped and gapless spin liquid phases, which are potentially realized in iridates and $\alpha$-RuCl$_3$. In the recent experiment of $\alpha$-RuCl$_3$, the signature of a nematic transition…
We first give a brief exposition of our recent realization of anyonic quantum states on single M5-brane probes in 11D super-gravity backgrounds, by non-perturbative quantization of the topological sector of the self-dual tensor field on the…
These are the lecture notes of the master's course "Quantum Computing", taught at Chalmers University of Technology every fall since 2020, with participation of students from RWTH Aachen and Delft University of Technology. The aim of this…
Programmable quantum simulators such as superconducting quantum processors and ultracold atomic lattices represent rapidly developing emergent technology that may one day qualitatively outperform existing classical computers. Yet, apart…
Classical topological concepts are applied to understand high performance computing simulations of molecules writhing in three dimensional space. These simulations produce peta-bytes of floating point data, to describe 3 dimensional changes…
We compute rigorously the ground and equilibrium states for Kitaev's model in 2D, both the finite and infinite version, using an analogy with the 1D Ising ferromagnet. Next, we investigate the structure of the reduced dynamics in the…
We investigate the robustness of topological phases in a Kitaev ladder composed of two coupled superconducting chains under the perturbing influence of a finite charge current. By introducing an effective Hamiltonian depending on the…
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…
We develop a supervised machine learning algorithm that is able to learn topological phases of finite condensed matter systems from bulk data in real lattice space. The algorithm employs diagonalization in real space together with any…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…