arXiv research

Flow-VQE uses generative flows to optimize VQE efficiently.

Paper connects knot invariants and Morse flow loops.

Quantum computers can simulate flow models efficiently.

Two new methods estimate quantum density matrices using machine learning.

Riemann moduli spaces are quantum ergodic for certain dimensions.

Perelman's Ricci flow emerges in quantum gravity, linking math and physics.

The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability density of the microscopical state is connected with a Perelman's functional of …

We discuss in rather general terms quantum field theories dealing with spaces of maps between Riemannian manifolds. In particular we explore the well--known connection between the renormalization group flow for non--linear sigma models and the Ricci flow.

Geodesic flows on Kähler manifolds are quantum integrable when metrics are c-projectively equivalent.

Quantum flag manifold σ-models are integrable and satisfy Ricci flow equations.

New topological quantum gravity theories linked to Ricci flow.

We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdière and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow of p implies quan…

The perturbative approach to nonlinear Sigma models and the associated renormalization group flow are discussed within the framework of Euclidean algebraic quantum field theory and of the principle of general local covariance. In particular we show in an Euclidean setting how to define Wick ordered powers of the underl…

Quantum propagation studied for Berezin-Toeplitz operators.

Study quantum diffusion on spectral triples and spinor bundles.

The paper adapts results for Reeb flows and Hamiltonian flows, showing all orbits are closed have identical periods.

Equivariant flows learn symmetrical distributions on manifolds.

We explore homotopies in quantum field theory formalism.

A new method for reconstructing flows from perturbed distributions.

We establish a direct classical-quantum correspondence on convex cocompact hyperbolic manifolds between the spectrums of the geodesic flow and the Laplacian acting on natural tensor bundles. This extends previous work detailing the correspondence for cocompact quotients.

The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the bulk renormalization group equation gives rise to the Ricci flow of target spac…

Study geometric quantization of Hamiltonian flows using Berezin-Toeplitz operators.

Quantum stochastic flow computes heat kernel traces for Ricci flat manifolds.

The paper proposes a method to sample quantum field configurations using neural operators and flows.

Unified geometric framework for quantum states using dual number algebras.

We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests…

Study of Ricci flow equations in topological quantum gravity.

Researchers use quantum chaos and RMT to analyze turbulence, revealing unique scaling laws.

This paper analyzes how kinetic terms in stock market equations can affect symmetry breaking.

The gradient flow of the Yang-Mills action acts pointwise on closed loops of gauge fields. We construct a topologically nontrivial loop of SU(2) gauge fields on S4 that is locally stable under the flow. The stable loop is written explicitly as a path between two gauge fields equivalent under a topologically nontrivial …

We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entro…

Renormalization in neural networks linked to quantum field theory.

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…

This is the first paper of a series in which we plan to study spectral asymptotics for sub-Riemannian Laplacians and to extend results that are classical in the Riemannian case concerning Weyl measures, quantum limits, quantum ergodicity, quasi-modes, trace formulae.Even if hypoelliptic operators have been well studied…

It is shown that 3D part of a spherically symmetric solution in conformal Weyl gravity interacting with Maxwell electrodynamics is a Yamabe flow as well. The Yamabe flow describes the transition from a horn of an initial wormhole to a 3D Euclidean space both filled with a radial electric field. It is supposed that such…

The Ricci flow has been of fundamental importance in mathematics, most famously though its use as a tool for proving the Poincaré Conjecture and Thurston's Geometrization Conjecture. It has a parallel life in physics, arising as the first order approximation of the Renormalization Group flow for the nonlinear sigma mod…

Let us consider a projective manifold and $Ω$ a volume form. We define the gradient flow associated to the problem of $Ω$-balanced metrics in the quantum formalism, the Ω$-balacing flow. At the limit of the quantization, we prove that the$Ω$-balacing flow converges towards a natural flow in Kähler geometry, the$Ω$-Kä…

Quantum models improve data generation from noisy quantum processors.

Consider $E$ a holomorphic vector bundle over a projective manifold $X$ polarized by an ample line bundle $L$. Fix $k$ large enough, the holomorphic sections $H^0(E\otimes L^k)$ provide embeddings of $X$ in a Grassmanian space. We define the \textit{balancing flow for bundles} as a flow on the space of projectively equ…

Given a solution of the (backwards) Ricci flow one can construct a so called canonical soliton metric on space-time, introduced by E. Cabezas-Rivas and P. Topping. We observe that for a mean curvature flow within a (backwards) Ricci flow background, the space-time track of the mean curvature flow yields a canonical sol…

New algorithm classifies and generates genomic sequences using RG-flow categorifier.

Paper explores Monge-Ampère in deep learning and quantum geometry.

Paper addresses optimization on Hadamard manifolds, generalizing gradient flow.

FlowMM models stable crystal structures efficiently.

Warm starts improve variational quantum algorithms by avoiding barren plateaus.

We prove the linear stability of Schwarzschild-Tangherlini spacetimes and their Anti-de Sitter counterparts under Ricci flow for a special class of perturbations. This is useful in the choice of suitable initial conditions in numerical Ricci-flow-based algorithms for obtaining new solutions to the Einstein equation whe…

Study explores quantum spaces on toric varieties and their limiting behavior.

Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci fl…