Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1406.2887 · New Journal of Physics

Focus on topological quantum computation

Jiannis K. Pachos, Steven H. Simon

Published Jun 10, 2014• 21 citations
arXivHTMLPDF

Abstract

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 the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches.

DOI
10.1088/1367-2630/16/6/065003

Related papers

4 Focus on topological quantum computation

Jiannis K. Pachos, Steven H. Simon

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 the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches.

•Jun 10, 2014•19 citations

Introduction to Topological Quantum Computation

Jiannis K. Pachos

Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.

Cambridge University Press eBooks•Apr 12, 2012•409 citations

Anyons and Topological Quantum Computation

Tudor D. Stanescu

Topological quantum computation has emerged as a rapidly growing research field at the confluence of physics, mathematics, and computer science, bringing together several major themes that fruitfully inform each other. Physics problems, ranging from fundamental questions concerning the foundations of quantum mechanics to problems regarding the classification, realization, and manipulation of topological phases of matter, and mathematical challenges, ranging from identifying the formal tools for the complete classification of topological phases to open problems in computational complexity, converge at this intellectual junction in a combined effort to realize fault-tolerant quantum computation. The convergence of these themes has a significance that goes beyond the simple realization of a certain application – even one as remarkable as a quantum computer – and generates a new paradigm in which the cross fertilization of ideas takes center stage. Thinking about topological quantum matter from the perspective of quantum computation is more creative and fruitful than simply asking the standard questions of many-body condensed matter physics. This is one of the main messages of this book, while the themes involved in this synergy represent its main subject. Therefore, it is fitting to conclude our journey with a chapter on the most explicit manifestation of this new paradigm: topological quantum computation.

CRC Press eBooks•May 3, 2024•0 citations

Anyon braiding statistics: From fundamental physics to scalable quantum computing

HE Jianhong, GAO Jie

Topological quantum computation aims to encode quantum information in the nonlocal degrees of freedom of non-Abelian anyons and manipulate it through braiding and fusion operations, offering a promising pathway to fault-tolerant quantum computation. Non-Abelian anyons, with their nontrivial braiding statistics and intrinsic topological fault tolerance, are regarded as a key building block for realizing scalable and decoherence-resistant quantum computing. This review systematically surveys the key developments in anyon physics over the past four decades, from the early theoretical prediction of fractional statistics to direct experimental verification of anyon braiding in fractional quantum Hall states. The physical principles and key findings of essential experimental schemes, including Fabry-Pérot interferometers, Mach-Zehnder interferometers, and anyon colliders, are comprehensively covered. Based on these foundations, the characterization of topological order in even-denominator fractional quantum Hall states, exemplified by the ν=5/2 state, and transport and interferometric probes of non-Abelian statistics are discussed in detail. Furthermore, recent advances in topological quantum states in novel material platforms, including graphene and twisted transition metal dichalcogenides, are reviewed, together with artificial quantum platforms that simulate non-Abelian braiding using superconducting quantum processors. Finally, the key challenges and future directions on the path from anyon physics to scalable topological quantum computing prototype devices are outlined.

•Sep 1, 2026•0 citations

Computational power of anyons

Jiannis K. Pachos

Topological quantum computation encodes and manipulates information by exclusively employing anyons. To study the computational power of anyons we plan to look into their fusion and braiding properties in a systematic way. This will allow us to identify a Hilbert space, where quantum information can be encoded fault-tolerantly. We also identify unitary evolutions that serve as logical gates. It is an amazing fact that fundamental properties, such as particle statistics, can be employed to perform quantum computation. As we shall see below, the resilience of these intrinsic particle properties against environmental perturbations is responsible for the fault-tolerance of topological quantum computation. Anyons are physically realised as quasiparticles in topological systems. Most of the quasiparticle details are not relevant for the description of anyons. This provides an additional resilience of topological quantum computation against errors in the control of the quasiparticles. In particular, the principles of topological quantum computation are independent of the underlying physical system. We therefore do not discuss its properties in this chapter. The abstraction might create a conceptual vacuum as many intrinsic properties of the system might appear to be absent. For example, we shall not be concerned with the trapping and transport of anyons or with geometrical characteristics of their evolutions. In this chapter we treat anyons as classical fundamental particles, with internal quantum degrees of freedom, much like the spin. Moreover, we assume that we have complete control over the topological system, in terms of initial-state preparation and final-state identification.

Cambridge University Press eBooks•Apr 12, 2012•0 citations

Topological Quantum Computation and Protected Gates

Sumit Sijher

This thesis serves to give a mathematical overview of topological quantum computation and to apply the theory to characterize desirable fault-tolerant operations called protected gates. Topological quantum computation is a novel paradigm for quantum computation which seeks to harness certain exotic quantum systems known as topological phases of matter that exhibit unique physical phenomena such as the manifestation of quasiparticle excitations called anyons. The low energy effective field theories of these systems can be expressed by certain topological quantum field theories, which in turn are described in terms of unitary modular tensor categories that capture the essential properties of a topological phase of matter and its corresponding anyon model. An overview of the relevant category theoretic concepts is given, and the axioms of a unitary modular tensor category are made explicit. A topological quantum field theory is then defined and used to describe topological quantum computation. Having developed the necessary theoretical background, the theory is then applied to characterize protected gates. The main result is a no-go theorem which states that, for any model, the set of protected gates is finite, and hence, cannot be used to do universal quantum computation using protected gates alone.

•Dec 22, 2015•0 citations
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 the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches.
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 the understanding of anyon properties inspired new quantum algorithms and helped in the characterization of topological phases of matter and their experimental realization. The conceptual appeal of topological systems as well as their promise for building fault-tolerant quantum technologies fuelled the fascination in this field. This 'focus on' collection brings together several of the latest developments in the field and facilitates the synergy between different approaches.
Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.
Topological quantum computation has emerged as a rapidly growing research field at the confluence of physics, mathematics, and computer science, bringing together several major themes that fruitfully inform each other. Physics problems, ranging from fundamental questions concerning the foundations of quantum mechanics to problems regarding the classification, realization, and manipulation of topological phases of matter, and mathematical challenges, ranging from identifying the formal tools for the complete classification of topological phases to open problems in computational complexity, converge at this intellectual junction in a combined effort to realize fault-tolerant quantum computation. The convergence of these themes has a significance that goes beyond the simple realization of a certain application – even one as remarkable as a quantum computer – and generates a new paradigm in which the cross fertilization of ideas takes center stage. Thinking about topological quantum matter from the perspective of quantum computation is more creative and fruitful than simply asking the standard questions of many-body condensed matter physics. This is one of the main messages of this book, while the themes involved in this synergy represent its main subject. Therefore, it is fitting to conclude our journey with a chapter on the most explicit manifestation of this new paradigm: topological quantum computation.
Topological quantum computation aims to encode quantum information in the nonlocal degrees of freedom of non-Abelian anyons and manipulate it through braiding and fusion operations, offering a promising pathway to fault-tolerant quantum computation. Non-Abelian anyons, with their nontrivial braiding statistics and intrinsic topological fault tolerance, are regarded as a key building block for realizing scalable and decoherence-resistant quantum computing. This review systematically surveys the key developments in anyon physics over the past four decades, from the early theoretical prediction of fractional statistics to direct experimental verification of anyon braiding in fractional quantum Hall states. The physical principles and key findings of essential experimental schemes, including Fabry-Pérot interferometers, Mach-Zehnder interferometers, and anyon colliders, are comprehensively covered. Based on these foundations, the characterization of topological order in even-denominator fractional quantum Hall states, exemplified by the ν=5/2 state, and transport and interferometric probes of non-Abelian statistics are discussed in detail. Furthermore, recent advances in topological quantum states in novel material platforms, including graphene and twisted transition metal dichalcogenides, are reviewed, together with artificial quantum platforms that simulate non-Abelian braiding using superconducting quantum processors. Finally, the key challenges and future directions on the path from anyon physics to scalable topological quantum computing prototype devices are outlined.
Topological quantum computation encodes and manipulates information by exclusively employing anyons. To study the computational power of anyons we plan to look into their fusion and braiding properties in a systematic way. This will allow us to identify a Hilbert space, where quantum information can be encoded fault-tolerantly. We also identify unitary evolutions that serve as logical gates. It is an amazing fact that fundamental properties, such as particle statistics, can be employed to perform quantum computation. As we shall see below, the resilience of these intrinsic particle properties against environmental perturbations is responsible for the fault-tolerance of topological quantum computation. Anyons are physically realised as quasiparticles in topological systems. Most of the quasiparticle details are not relevant for the description of anyons. This provides an additional resilience of topological quantum computation against errors in the control of the quasiparticles. In particular, the principles of topological quantum computation are independent of the underlying physical system. We therefore do not discuss its properties in this chapter. The abstraction might create a conceptual vacuum as many intrinsic properties of the system might appear to be absent. For example, we shall not be concerned with the trapping and transport of anyons or with geometrical characteristics of their evolutions. In this chapter we treat anyons as classical fundamental particles, with internal quantum degrees of freedom, much like the spin. Moreover, we assume that we have complete control over the topological system, in terms of initial-state preparation and final-state identification.
This thesis serves to give a mathematical overview of topological quantum computation and to apply the theory to characterize desirable fault-tolerant operations called protected gates. Topological quantum computation is a novel paradigm for quantum computation which seeks to harness certain exotic quantum systems known as topological phases of matter that exhibit unique physical phenomena such as the manifestation of quasiparticle excitations called anyons. The low energy effective field theories of these systems can be expressed by certain topological quantum field theories, which in turn are described in terms of unitary modular tensor categories that capture the essential properties of a topological phase of matter and its corresponding anyon model. An overview of the relevant category theoretic concepts is given, and the axioms of a unitary modular tensor category are made explicit. A topological quantum field theory is then defined and used to describe topological quantum computation. Having developed the necessary theoretical background, the theory is then applied to characterize protected gates. The main result is a no-go theorem which states that, for any model, the set of protected gates is finite, and hence, cannot be used to do universal quantum computation using protected gates alone.