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.
Quantum machine learning models can approximate any continuous function.
Quantum theory of curved tetrahedrons yields quantum group intertwiners.
Defines coherent manifolds and their quantum applications.
Quantum autoencoders allow for reducing the amount of resources in a quantum computation by mapping the original Hilbert space onto a reduced space with the relevant information. Recently, it was proposed to employ approximate quantum adders to implement quantum autoencoders in quantum technologies. Here, we carry out …
Quantum machine learning model for binary classification.
Quantum machine learning classification depends on mutual informations between state and parameter spaces.
We derive the quantum Teichmüller space, previously constructed by Kashaev and by Fock and Chekhov, from tensor products of a single canonical representation of the modular double of the quantum plane. We show that the quantum dilogarithm function appears naturally in the decomposition of the tensor square, the quantum…
A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and analyzed. This includes Laplace and Dirac operators, quantum versions of Clifford …
To give a Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on the extended quantum 3d space is extended by introducing inner derivations and Lie derivatives.
Quantum groups created from disk configuration space homologies.
Quantum neural networks generalize better due to flatter parameter space.
Quantum isometry groups extend to all countable metric spaces, and loose embeddings help understand metric space relationships.
QCML uses quantum geometry to represent data.
Estimates quantum cohomology complexity for Fano varieties and homogeneous spaces.
Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for cla…
In this note we show that the Riemann moduli spaces equipped with the Weil--Petersson metric are quantum ergodic for . We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.
Quantum SVM improves financial data classification.
Quantum variational circuits improve reinforcement learning efficiency.
Quantum algorithms speed up reinforcement learning policies in large state-action spaces.
Quantum kernels offer potential speed-ups but require encoding problem-specific knowledge.
Quantum connections replace metrics with operator inner products.
Quantum-assisted VAE improves similarity search in high-dimensional datasets.
Paper defines compact quantum spaces with Kähler structures.
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…
This work constructs a finite-dimensional projective representation for a quantum Teichmüller model.
We compute the classical and quantum cohomology rings of the twistor spaces of 6-dimensional hyperbolic manifolds and the eigenvalues of quantum multiplication by the first Chern class. Given a half-dimensional totally geodesic submanifold we associate, after Reznikov, a monotone Lagrangian submanifold of the twistor s…
Quantum computer method for pricing rainbow options efficiently.
We compute Stokes matrices and monodromy for the quantum cohomology of projective spaces. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves.
Quantum traces embed into quantum tori for surface skein algebras.
New framework for quantum invariants of 3-manifolds using homology.
Quantum trace maps for surfaces are shown to be compatible under triangulations.
Derives Atiyah sequence for noncommutative bundles.
QGAA learns latent quantum states, reducing errors in quantum data generation.
We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichmüller space of a marked surface, defined by Chekhov-Fock (and Kashaev) in an abstract …
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…
Unified geometric approach to quantum indeterminacy.
Explains quantum cohomology of Grassmannians using tt* equations.
We define the quantum correction of the Teichmüller space of Calabi-Yau manifolds. Under the assumption of no weak quantum correction, we prove that the Teichmüller space is a locally symmetric space with the Weil-Petersson metric. For Calabi-Yau threefolds, we show that no strong quantum co…
In this chapter, we survey the algebraic aspects of quantum Teichmüller space, generalized Kashaev algebra and a natural relationship between the two algebras.
The objective of this paper is to clarify the relationships between the quantum D-module and equivariant Floer theory. Equivariant Floer theory was introduced by Givental in his paper ``Homological Geometry''. He conjectured that the quantum D-module of a symplectic manifold is isomorphic to the equivariant Floer cohom…
Quantum kernels can be efficiently embedded into classical feature spaces.
Study evaluates capacity and trainability of parametrized quantum circuits.
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Ha…
Quantum Kirwan maps between K-theories of G-varieties and GIT quotients.
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive th…
Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion is introduced to simplify the algorithm for quantum LS-SVM, while retaining expo…
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the…
Quantum computers can enhance spectral methods in machine learning.