A Short Introduction to Topological Quantum Computation

2017/05/11 by Ville Lahtinen, Jiannis K. Pachos, Jiannis Pachos · 1 voice · 228 citations
Computer Science · Physics and Astronomy · #Anyon #Context (archaeology) #MAJORANA #Quantum #Quantum Computing Algorithms and Architecture #Quantum algorithm #Quantum computer #Quantum many-body systems #Quantum network #Quantum technology #Topological Materials and Phenomena #Topological quantum computer #Topology (electrical circuits) #cond-mat.mes-hall #quant-ph

paper · pdf · open access · doi:10.21468/scipostphys.3.3.021

published in SciPost Physics 3(3) (SciPost.org) · v4: typos corrected, published version

openalex created_date 2017/08/08 · openalex publication_date 2017/09/09 · arxiv created 2017/09/12 · arxiv updated 2017/09/14 · openalex updated_date 2026/08/05

Abstract

This review presents an entry-level introduction to topological quantum computation -- quantum computing with anyons. We introduce anyons at the system-independent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. Both the encoding and the processing are inherently resilient against errors due to their topological nature, thus promising to overcome one of the main obstacles for the realisation of quantum computers. We outline the general steps of topological quantum computation, as well as discuss various challenges faced by it. We also review the literature on condensed matter systems where anyons can emerge. Finally, the appearance of anyons and employing them for quantum computation is demonstrated in the context of a simple microscopic model -- the topological superconducting nanowire -- that describes the low-energy physics of several experimentally relevant settings. This model supports localised Majorana zero modes that are the simplest and the experimentally most tractable types of anyons that are needed to perform topological quantum computation.

Citations

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond

Cited by

• Noninteracting tight-binding models for Fock parafermions
• Covariance Geometry of Basis-Resolved Low-Energy Wavefunctions in the Spin-1/2 Kitaev--Heisenberg Model
• Floquet Bosonic Kitaev Chain
• Classical shadows for sample-efficient measurements of gauge-invariant observables
• Majorana current induced by charge current in Kitaev magnet/graphene bilayers
• Secret communication games and a hierarchy of quasiparticle statistics in 3 + 1D topological phases
• One-dimensional topological superconductors with nonsymmorphic symmetries
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• Continuous measurement-based holonomic quantum computation
• Topological superconductivity in a dimerized Kitaev chain revealed by nonlocal transport
• Zero and Nonzero Energy Majorana Modes in an Extended Kitaev Chain
• Majorana braiding simulations with projective measurements
• Measuring coherence factors of states in superconductors through local current
• Topologically nontrivial multicritical points
• Robustness of the flux-free sector of the Kitaev honeycomb against environment
• A Toy Model for Topological Entanglement Features in 1+1D Integrable Quantum Field Theory
• A higher dimensional generalization of the Kitaev spin liquid
• Robustness of topological edge states in alternating spin chains against environment
• NonHermitian Topological Phases in a Hermitian Modified Bosonic Kitaev Chain
• The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm
• Local Information Flow in Quantum Quench Dynamics
• Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode
• Graph-state representation of the toric code
• Combating quasiparticle poisoning with multiple Majorana fermions in a periodically-driven quantum wire
• Simulating quantum many-body dynamics on a current digital quantum computer
• Quantum gates for Majoranas zero modes in topological superconductors in one-dimensional geometry
• Universal fault-tolerant measurement-based quantum computation
• Fibonacci Anyons Versus Majorana Fermions: A Monte Carlo Approach to the Compilation of Braid Circuits in SU(2)k Anyon Models
• Non-Abelian braiding in spin superconductors utilizing the Aharonov-Casher effect
• Excitations in the field-induced quantum spin liquid state of α-RuCl3
• Tri-component-pairing chiral superconductivity on the honeycomb lattice with mixed s- and d-wave symmetries
• Majorana Zero Modes in Ferromagnetic Wires without Spin-Orbit Coupling

Discussions

• Introduction to Topological Quantum Computation [hn, 66 points, 5 comments]

Related

• Quantum Computing with ℤ₂ Abelian anyon system
• Quantum Field Theories, Topological Materials, and Topological Quantum Computing
• Topological Quantum Computation
• Introduction to Topological Quantum Computation
• Non-Abelian anyons and topological quantum computation