Topological quantum gates in homotopy type theory

DOI10.1007/s00220-024-05020-8MaRDI QIDQ6584358

David Jaz Myers, Urs Schreiber, H. Sati

Publication date: 6 August 2024

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

Quantum field theory; related classical field theories (81Txx) Foundations, quantum information and its processing, quantum axioms, and philosophy (81Pxx) Type theory (03B38)

Cites Work

• Periodic table for topological insulators and superconductors
• On the adiabatic theorem of quantum mechanics
• Anyons
• Braids, Links, and Mapping Class Groups. (AM-82)
• Infinite loop space theory
• Spaces of partial maps, fibred mapping spaces and the compact-open topology
• Infinite Loop Spaces (AM-90)
• Explicit Connection Between Conformal Field Theory and 2+1 Chern–Simons Theory
• Quantum computations: algorithms and error correction
• THE WALL OF THE CAVE
• Cohesive Toposes and Cantor's 'lauter Einsen'
• On the Power of Quantum Computation
• P/NP , and the quantum field computer
• Setoids in type theory
• Principles of Quantum Computation and Information
• Cubical Type Theory: a constructive interpretation of the univalence axiom
• Higher Categories and Homotopical Algebra
• Weil's Conjecture for Function Fields
• Eilenberg-MacLane spaces in homotopy type theory
• A Mechanization of the Blakers-Massey Connectivity Theorem in Homotopy Type Theory
• Brouwer's fixed-point theorem in real-cohesive homotopy type theory
• Berry Phases in Electronic Structure Theory
• A Brief, Subjective History of Homology and Homotopy Theory in This Century
• Topological quantum computation
• GAUGE FIELDS AND SPACE-TIME
• Towards a quantum programming language
• Propositions as [Types]
• On the Cauchy Completeness of the Constructive Cauchy Reals
• Quantum Gauge Field Theory in Cohesive Homotopy Type Theory
• Quantum Information Theory
• Introducing Design Automation for Quantum Computing
• Cubical Agda: A dependently typed programming language with univalence and higher inductive types
• Modal descent
• Validating Mathematical Structures
• The law of excluded middle in the simplicial model of type theory
• Higher Groups in Homotopy Type Theory
• On Higher Inductive Types in Cubical Type Theory
• A Higher Structure Identity Principle
• HOMOLOGICAL REPRESENTATIONS OF BRAID GROUPS AND KZ CONNECTIONS
• Modalities in homotopy type theory
• From Categories to Homotopy Theory
• Mathematics of topological quantum computing
• Type Theory and Homotopy
• Abelian Groups
• The General Universal Property of the Propositional Truncation
• Introduction to Topological Quantum Matter & Quantum Computation
• Abstract Homotopy Theory
• Homotopy Type Theory: Univalent Foundations of Mathematics
• Towards Constructive Homological Algebra in Type Theory
• Why should anyone care about computing with anyons?
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Higher Topos Theory (AM-170)
• Configuration Spaces.
• The Exponential Law of Maps I
• Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems
• Abstract homotopy theory and generalized sheaf cohomology
• The Braid Groups.
• Sets in homotopy type theory
• Univalence for inverse diagrams and homotopy canonicity
• Introduction to homotopy theory
• Simplicial homotopy theory
• On the De Rham cohomology of algebraic varieties
• String theory and quark confinement
• A homotopy bigroupoid of a topological space
• Higher Structures in M‐Theory
• The Rational Higher Structure of M‐theory
• M/F-theory as Mf-theory
• Eilenberg-MacLane spaces and stabilisation in homotopy type theory
• Univalent Foundations and the Equivalence Principle
• Fundamental weight systems are quantum states
• Anyonic topological order in twisted equivariant differential (TED) K-theory
• The Character Map in Non-abelian Cohomology
• Anyonic defect branes and conformal blocks in twisted equivariant differential (TED) K-theory
• Differential cohomology theories as sheaves of spectra
• Interpretation of constructive multi-typed theory in the theory of arithmetical truth
• Differential geometry and mathematical physics. II: Fibre bundles, topology and gauge fields
• Twisted equivariant matter
• Twisted differential string and fivebrane structures
• Homotopical algebraic geometry. I: Topos theory
• Mathematische Grundlagen der Quantenmechanik.
• Adiabatic theorems and applications to the quantum Hall effect
• Conformal field theory
• Notes on Landauer's principle, reversible computation, and Maxwell's demon
• Isomorphism is equality
• Telescopic mappings in typed lambda calculus
• Anyons in an exactly solved model and beyond
• Lectures on the Curry-Howard isomorphism
• Principal \(\infty \)-bundles: general theory
• Algebraic topology
• Transformation groups
• Constructivism in mathematics. An introduction. Volume II
• Comprehension categories and the semantics of type dependency
• Categorical logic and type theory
• Constructive mathematics: a foundation for computable analysis
• On algebraic equations satisfied by hypergeometric correlators in WZW models. I
• Inductive families
• Representing inductively defined sets by wellorderings in Martin-Löf's type theory
• Sheaves in topology
• Theorie der Zöpfe.
• Principia Mathematica. Vol. I.
• Zur Deutung der intuitionistischen Logik
• Holonomic quantum computation
• Algebraic topology from a homotopical viewpoint
• The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines
• Univalent foundations as structuralist foundations
• Introduction to abelian and non-abelian anyons
• A modular functor which is universal for quantum computation
• Fault-tolerant quantum computation by anyons
• Regularity of the category of Kelley spaces
• Stacks of group representations.
• The simplicial model of univalent foundations (after Voevodsky)
• Combinatorial parametrised spectra
• Fusion structure from exchange symmetry in (2+1)-dimensions
• Equivariant cohomotopy implies orientifold tadpole cancellation
• Differential KO-theory: constructions, computations, and applications
• Revisiting the categorical interpretation of dependent type theory
• Ultraproducts in the theory of models
• Large \(N\) field theories, string theory and gravity
• Tool and object. A history and philosophy of category theory
• On the differential equations satisfied by period matrices
• On the differentiation of De Rham cohomology classes with respect to parameters
• Homotopical algebra
• Principles of intuitionism. Lectures presented at the summer conference on intuitionism and proof theory (1968) at SUNY at Buffalo, NY
• Equations différentielles à points singuliers réguliers
• The geometry of iterated loop spaces
• Configuration-spaces and iterated loop-spaces
• A formulation of the simple theory of types.
• Untersuchungen über das logische Schließen. I.
• Higher structures in geometry and physics. In honor of Murray Gerstenhaber and Jim Stasheff
• The logic of quantum mechanics
• Homology with local coefficients
• Ising-like and Fibonacci anyons from KZ-equations
• Large \(k\) topological quantum computer
• Differential cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
• Groupoids: unifying internal and external symmetry. A tour through some examples.
• Practical foundations for programming languages
• Introduction to representations of braid groups
• Categorical Homotopy Theory
• Introduction to Topological Quantum Computation
• An ∞-categorical approach to R -line bundles, R -module Thom spectra, and twisted R -homology
• π n (S n ) in Homotopy Type Theory
• Identity in Homotopy Type Theory, Part I: The Justification of Path Induction
• Inductive Types in Homotopy Type Theory
• Quantum computational networks
• Quantum Computation and Quantum Information
• Non-Abelian anyons and topological quantum computation
• Rings and Their Modules
• Types are weak ω -groupoids
• Some Properties of Finitely Presented Groups with Topological Viewpoints
• Quantum Computation as Geometry
• On the rapid computation of various polylogarithmic constants
• Homotopy-Initial Algebras in Type Theory
• HYPERGEOMETRIC-TYPE INTEGRALS AND THE $\mathfrak{sl}(2, {\rm C})$ KNIZHNIK-ZAMOLODCHIKOV EQUATION
• The adiabatic theorem in a quantum many-body setting
• Locally cartesian closed categories and type theory
• Constructive analysis, types and exact real numbers
• A monadic, functional implementation of real numbers
• Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation
• Quantal phase factors accompanying adiabatic changes
• Homotopy theoretic models of identity types
• Dependently Typed Programming in Agda

This page was built for publication: Topological quantum gates in homotopy type theory

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6584358)