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Some Aspects of Mathematical and Physical Approaches for Topological Quantum Computation
Authors: V. Kantser
Keywords: topological computation, braided strings, anyons, topological phase, braiding, wire networks
– 0.18 Mb
Keywords: topological computation, braided strings, anyons, topological phase, braiding, wire networks
Abstract
A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin braid group – the mathematical basis of topological quantum computation (TQC). Vector spaces of TQC correspond to associated strings of particle interactions, and TQC operates its calculations on braided strings of special physical quasiparticles – anyons – with non-Abelian statistics. The physical platform of TQC is to use the topological quantum numbers of such small groups of anyons as qubits and to perform operations on these qubits by exchanging the anyons, both within the groups that form the qubits and, for multi-qubit gates, between groups. By braiding two or more anyons, they acquire up a topological phase or Berry phase similar to that found in the Aharonov-Bohm effect. Topological matter such as fractional quantum Hall systems and novel discovered topological insulators open the way to form system of anyons – Majorana fermions – with the unique property of encoding and processing quantum information in a naturally fault-tolerant way. In the topological insulators, due to its fundamental attribute of topological surface state occurrence of the bound, Majorana fermions are generated at its heterocontact with superconductors. One of the key operations of TQC – braiding of non-Abelian anyons: it is illustrated how it can be implemented in one-dimensional topological isolator wire networks.Institute of the Electronic Engineering and Nanotechnologies "D. Ghitu",
Academy of Sciences, Academiei str. 3/3,
MD 2028 Chisinau, Moldova,
E-mail:
Academy of Sciences, Academiei str. 3/3,
MD 2028 Chisinau, Moldova,
E-mail:
Fulltext
– 0.18 Mb
Contents
- Preface
- Constantin Gaindric (in honour of his 70th birthday)
- Designing and Building Modern Information Systems; A Series of Decisions to Be Made
- Romanian Linguistic Resources On Very Large Scale
- Natural Language Question Answering in Open Domains
- Analysis and Modeling of Vapor Recompressive Distillation Using ASPEN-HYSYS
- Prediction Models of Financial Markets Based on Multiregression Algorithms
- A New Foundation For Knowledge Systems
- Some Aspects of Mathematical and Physical Approaches for Topological Quantum Computation
- Tool Means of Organization and Support of Electronic Services to the Population
