Quantum physics model uses knot theory for fragile topology.
problem Modeling quantum physics' fragile topology.
method Knot theoretic algorithm.
result Quantum physics' fragile topology modeled.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
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48 results for “Quantum topology”
Study topological quantum mechanics on orbifolds with geometric interpretation.
problem Quantum mechanical models on symplectic orbifolds.
method Explicit orbifold version of quantum HKR map and exact semi-classical approximation.
result Geometric and quantum field theoretic interpretation of orbifold algebraic index.
Topological quantum computers use hyperbolic knots for computations.
problem The difficulty of calculating quantum invariants of knots.
method Using hyperbolic knots to compute topological quantum computer invariants.
result The hyperbolic geometry of knots is unlikely to be useful for topological quantum computation.
New stable homotopy refinement of quantum annular Khovanov homology.
problem Quantum topological Hochschild homology and annular Khovanov spectra.
method Introducing quantum topological Hochschild homology (qTHH) and constructing a new stable homotopy refinement of quantum annular Khovanov homology.
result The new stable homotopy refinement agrees with qTHH of spectral Chen-Khovanov tangle bimodules and recovers earlier work.
We present two paradigms relating algebraic, topological and quantum computational statistics for the topological model for quantum computation. In particular we suggest correspondences between the computational power of topological quantum computers, computational complexity of link invariants and images of braid grou…
Kauffman and Lomonaco explored the idea of understanding quantum entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of G. Alagic, M. Jarret, and S. Jordan it is shown that entanglement is a necessary condit…
Novel framework explains generalization in deep neural networks.
problem Understanding and improving generalization in deep neural networks.
method Topological Quantum Neural Networks as the semi-classical limit of Deep Neural Networks.
result Demonstrates that the perceptron, viewed as the semi-classical limit, achieves similar results to standard neural networks without training.
New framework for quantum invariants of 3-manifolds using homology.
problem Quantum invariants of 3-manifolds.
method Homological construction of mapping class group representations extended to cobordisms.
result Construction of a -dimensional TQFT assigning twisted homology to surfaces.
Develops Hermitian TQFTs from quantum groups, defining new topological phases.
problem Defining Hermitian non-semisimple TQFTs.
method Categorical context and representation theory of quantum groups.
result New pseudo-Hermitian topological phases from quantum group representations.
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
Abelian Chern-Simons theorymath.DG
We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been previously explored in connection to the nonabelian Chern-Simons theory [JW,ADW]. We f…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned topological models ha…
Researchers prove quantum invariants remain hard even when restricted.
problem Computing quantum invariants on 3-manifolds with specific restrictions.
method Using Heegaard splittings and Hempel distance, they construct a hyperbolic 3-manifold with same invariant.
result Proving hardness of computing quantum invariants is preserved under specific restrictions.
Universal Braiding Quantum Gatesquant-ph
Simple construction for universal quantum gates.
problem Designing efficient quantum gates for topological computers.
method Demonstrated a simple construction for unitary solutions of the braided Yang-Baxter equation in any dimension.
result Proved the existence of universal quantum gates in any dimension.
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime dimension…
This paper introduces quantum invariants for 3-alterfolds and proves their consistency with topological moves.
problem Quantum invariants for 3-alterfolds and their consistency with topological moves.
method Introduction of 3-alterfolds with embedded separating surfaces and spherical fusion categories.
result Quantum invariants of 3-alterfolds are consistent with topological moves and generalize invariants of 3-manifolds containing framed links.
Study uses big data to analyze quantum invariants.
problem Investigate structural properties of Jones polynomial.
method Exploratory and topological data analysis, including coloring, rank increase, categorification.
result Contrasts behavior of Jones polynomial under various enhancements.
Modified Hennings invariant defined using quantum groups and integrals.
problem Defining a modified Hennings invariant using quantum groups.
method Topological ribbon Hopf algebra, discrete Fourier transforms, symmetrized graded integral, modified trace.
result Modified graded Hennings invariant defined and extended to empty manifolds.
The paper explores mapping class groups and their quantum field theory representations.
problem Understanding finite dimensional representations of mapping class groups.
method Survey of topological quantum field theory aspects.
result Discussion of finite dimensional representations in quantum field theory.
Quantum cellular automata form a homology theory.
problem Understanding the topological structure of quantum cellular automata.
method Formal properties of coarse homology theories.
result Quantum cellular automata naturally form the degree-zero part of a coarse homology theory.
We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.
We define some new invariants for 3-manifolds using the space of taut codim-1 foliations along with various techniques from noncommutative geometry. These invariants originate from our attempt to generalise Topological Quantum Field Theories in the Noncommutative geometry / topology realm.
Link homology theories connect to 4-manifold invariants and TQFTs.
problem Connecting link homology theories to 4-manifold invariants and TQFTs.
method Functorial link homologies, skein modules, handle decompositions.
result Link homology theories become diagram-independent and furnish invariants of 4-manifolds.
We give a topological formula of the loop expansion of the colored Jones polynomials by using identification of generic quantum sl2 representation with homological representations. This gives a direct topological proof of the Melvin-Morton-Rozansky conjecture, and a connection between entropy of braids and quantum repr…
A surprising image of the stock market arises if the price time series of all Dow Jones Industrial Average stock components are represented in one chart at once. The chart evolves into a braid representation of the stock market by taking into account only the crossing of stocks and fixing a convention defining overcros…
Tropical geometry aids in computing topological quantum field theories.
problem Computing Gromov-Witten invariants using tropical geometry.
method Using mathematical techniques of tropical geometry to compute topological quantum field theories of pseudoholomorphic maps.
result Identifies the tropicalization of localization equations and studies the geometry and symmetries of the theory.
Quantum invariants of 3-manifolds and links reviewed, with connections to other topological invariants.
problem Quantum invariants of 3-manifolds and links.
method Review of recent developments and connections to other invariants.
result Rich features of quantum invariants like quantum modularity and Verma module structures.
We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3-manifold (closed, oriented and connected) and not only to homology 3-spheres. There is also a physical motivation: one would like to construct a nonco…
Operads and moduli spacesmath.GT
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions of 'quantum invariants' of manifolds inspired by ideas originating from physics.…
Perelman's Ricci flow emerges in quantum gravity, linking math and physics.
problem Understanding Perelman's Ricci flow equations in quantum gravity.
method Mapping Perelman's Ricci flow equations to localization equations in topological quantum gravity.
result Perelman's dilaton and fixed volume condition emerge dynamically.
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms …
Neumann's work connects 3-manifold invariants to quantum topology.
problem Understanding invariants of 3-manifolds.
method Ideal triangulations, volume, Chern-Simons invariants, Bloch group.
result Neumann's work bridges classical invariants to quantum topology.
A quantum N-dimer modelmath.QA
Quantum model for knotted graphs from knot theory.
problem Constructing an isotopy invariant polynomial for knotted bipartite ribbon graphs.
method Applying quantum topology to construct an isotopy invariant polynomial.
result Computed the expected number of loops in the double dimer model.
The Jones-Wenzl projectors play a central role in quantum topology, underlying the construction of SU(2) topological quantum field theories and quantum spin networks. We construct chain complexes whose graded Euler characteristic is the "classical" projector in the Temperley-Lieb algebra. We show that they are homotopy…
We present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted …
We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)-dimensional unoriented topological quantum field theories to Bar-Natan's geometric formalism to define new theories for stable equivalence classes.
On Quantum Indeterminacyquant-ph
Unified geometric approach to quantum indeterminacy.
problem Quantum indeterminacy and uncertainty principles.
method Geometric formulation using convex geometry and symplectic topology.
result Robertson-Schrodinger inequalities emerge as geometric principles.
TQFTs and quantum computingquant-ph
Program connects quantum computing and topological field theories.
problem Connecting quantum computing and topological field theories.
method Formalizes the connection using cobordisms and parallel transport.
result Realizes quantum circuits as cobordisms in a double category.
The moduli space of isometry classes of Riemannian structures on a smooth manifold was emphasized by J.A.Wheeler in his superspace formalism of quantum gravity. A natural question concerning it is: What is a natural topology on such moduli space that reflects best quantum fluctuations of the geometries within the Planc…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold. However, as Donaldson-Witten theory (a topological quantum field theory but not a…
This paper provides a topological interpretation for number theoretic properties of quantum invariants of 3-manifolds. In particular, it is shown that the p-adic valuation of the quantum SO(3)-invariant of a 3-manifold M, for odd primes p, is bounded below by a linear function of the mod p first betti number of M. Shar…
We show that the topological modular functor from Witten-Chern-Simons theory is universal for quantum computation in the sense a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern-Simons theory at a fifth ro…
Defines a map connecting 3d-index and skein module.
problem Connecting mathematical physics predictions with topological quantum field theory.
method Defines a map from skein module to Laurent series ring.
result The map fulfills a supersymmetry prediction and is part of a conjectural topological quantum field theory.
Graph potentials link to topological QFTs, with computational methods.
problem Defining a topological quantum field theory using graph potentials.
method Using colored trivalent graphs and birational type to define a topological QFT.
result Graph potentials' birational type depends on the graph's homotopy type.
Estimates quantum cohomology complexity for Fano varieties and homogeneous spaces.
problem Quantum cohomology complexity estimation for compact symplectic manifolds.
method Estimates the number of states with finite approximate complexity for Fano complete intersections and (co)minuscule homogeneous varieties.
result Sharp upper bound for the dimension of the space spanned by states with finite complexity for Gr(2, n).
Modified knotoids with framing and coframing for quantum invariants.
problem Defining and classifying knotoids with framing.
method Defining framed and biframed knotoids, showing topological correspondence, and constructing quantum invariants.
result Generalized quantum knotoid invariants constructed.
A quantum field theory for Spin(7)-instantons derived from moduli spaces.
problem Constructing a topological quantum field theory for Spin(7)-instantons.
method Using Mathai-Quillen formalism and AKSZ formalism, we derive the action and Batalin-Vilkovisky action.
result The Batalin-Vilkovisky action matches the Mathai-Quillen construction and provides a framework for classical observables.