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.
Finiteness predicts dualities in quantum gravity.
Quantum machine learning for 2D classification tasks using optimized feature maps.
Estimates quantum cohomology complexity for Fano varieties and homogeneous spaces.
This work constructs a finite-dimensional projective representation for a quantum Teichmüller model.
A quantum system can be entirely described by the Kähler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we give an explicit link between the geometrical formulation (of finite dimensional qua…
We present a finite-dimensional version of the quantum model for the stock market proposed in [C. Zhang and L. Huang, A quantum model for the stock market, Physica A 389(2010) 5769]. Our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical for…
Study of quantum Riemannian geometries over binary field, finding many non-flat examples.
Unveils fermions' geometric nature in the Standard Model as noncommutative forms.
Arithmetic Dijkgraaf-Witten theory constructs analogues in Chern-Simons TQFT.
We discuss the construction of finite noncommutative geometries on Hopf algebras and finite groups in the `quantum groups approach'. We apply the author's previous classification theorem, implying that calculi in the factorisable case correspond to blocks in the dual, to classify differential calculi on the quantum cod…
Renormalization in neural networks linked to quantum field theory.
Paper defines compact quantum spaces with Kähler structures.
Unified geometric framework for adiabatic quantum mechanics.
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…
Quantum systems on coadjoint orbits yield spectra matching Dolbeault and de Rham indices.
Quantum cohomology gives a finite dimensional integrable system via the Dubrovin connection. Motivated by Givental's work on mirror symmetry, we use gauge theory techniques and the Frobenius Integrability Theorem to find flat sections for the Dubrovin connection. An explicit calculation is given for projective space.
We investigate the representation theory of the polynomial core of the quantum Teichmuller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell decompositions of S. Our main result is that irreducible finite-dimensional represent…
Extends quantum annular homology to infinite sets.
The price of a given stock is exactly known only at the time of sale when the stock is between the traders. If we know the price (owner) then we have no information on the owner (price). A more general description including cases when we have partial information on both price and ownership is obtained by using the quan…
Classifies state functions for framed tangles in a disk.
Quantum traces embed into quantum tori for surface skein algebras.
New algorithms learn MDPs with better regret bounds using generative sampling.
Holomorphic structures on quantum flag manifolds uniquely defined.
The paper analyzes how quantum PageRank changes with small perturbations.
Authors use exotic 4-manifolds to model quantum computing and measurements.
The paper explores mapping class groups and their quantum field theory representations.
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to define a dynamic-dependent metric tensor on the principal manifold, such that the…
Quantum Fourier Transform aids machine learning inference.
We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified by classical geometric data. We also investigate the family of intertwining opera…
We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kaehler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. W…
New learning rule for quantum measurement classes overcomes uniform convergence issues.
Improved formulation of spinfoam quantum gravity with cosmological constant, ensuring all amplitudes are finite and providing semiclassical asymptotics.
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum composite systems we discuss and give examples of measures of entanglement.
The category of finite dimensional module over the quantum superalgebra U_q(sl(2|1)) is not semi-simple and the quantum dimension of a generic U_q(sl(2|1))-module vanishes. This vanishing happens for any value of q (even when q is not a root of unity). These properties make it difficult to create a fusion or modular ca…
Quantum computing speeds up pricing multi-asset derivatives.
Center identified in stated skein algebra for quantum traces.
In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and its instantaneous forward time derivative, even if we consider it as a continuous …
Jordan algebras in information geometry linked to metrics on probability distributions.
Finite presentations for skein algebras linked to gauge field theory.
Program connects quantum computing and topological field theories.
M. Hennings and G. Kuperberg defined quantum invariants Z_{Henn} and Z_{Kup} of closed oriented 3-manifolds based on certain Hopf algebras, respectively. We prove that |Z_{Kup}|=|Z_{Henn}|^2 for lens spaces when both invariants are based on factorizable finite dimensional ribbon Hopf algebras.
Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.
We report on recent results of the authors concerning calculations of quantum invariants of Seifert 3-manifolds. These results include a derivation of the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated with an arbitrary complex finite dimensional simple Lie algebra, and a determination of th…
Study of webs in quantum type C, proving equivalence to quantum representations.
This paper outlines an approach to the non-abelian theta functions of the -Chern-Simons theory with the methods used by A. Weil for studying classical theta functions. First we translate in knot theoretic language classical theta functions, the action of the finite Heisenberg group, and the discrete Fourier tran…
Quantum states associated with subsets of product manifolds are separable.
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil contruction of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dim…