arXiv subjects

Pablo Páez-Velasco

Publications and source records attributed to Pablo Páez-Velasco.

3 recordsLinked to original sources

arXiv2026

Rapid mixing for Gibbs measures in Riemannian manifolds

Langevin dynamics on Riemannian manifolds is analyzed. Conditions ensuring the existence of a suitable logarithmic Sobolev inequality (rapid mixing to the Gibbs measure) are identified. These conditions involve the curvature of the manifold, the inverse temperature, escaping directions from saddle points, and exclude barren plateaus and spurious local minima. We show that when these conditions are met, mixing times polynomial in the dimension of the manifold are achievable. This result is obtained through a relation between Langevin processes in the domain and in the image of a Riemannian submersion. Such a relation can be of independent interest.

math-ph↗

arXiv2026

Tensor network manifolds and Riemannian fundamental theorem for tensor networks

Tensor networks provide a powerful framework for efficiently representing high-dimensional data and many-body quantum states. Endowing tensor networks with a Riemannian manifold structure provides a natural setting for numerical optimization and analysis. A central feature of tensor networks is their gauge freedom, whose characterisation (captured by so-called fundamental theorems) underlies both their intrinsic structure and the design of numerical algorithms. In this work, we study the interaction between the Riemannian manifold structure and the gauge freedom for several families of tensor networks. Using group actions and Riemannian submersions, we establish a Riemannian fundamental theorem for the tensor network families studied.

math-ph↗

arXiv2026

Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains

We introduce the notion of polynomial-depth duality transformations, which relates two sets of operator algebras through a conjugation by a poly-depth quantum circuit, and make use of this to construct efficient Gibbs samplers for a variety of interesting quantum Hamiltonians as they are poly-depth dual to classical Hamiltonians. This is for example the case for the 2D toric code, which is demonstrated to be poly-depth dual to two decoupled classical Ising spin chains for any system size, and we give evidence that such dualities hold for a wide class of stabilizer Hamiltonians. Additionally, we extend the above notion of duality to Lindbladians in order to show that mixing times and other quantities such as the spectral gap or the modified logarithmic Sobolev inequality are preserved under duality.

quant-ph↗