Computation of entanglement for quantum states by a Consensus-Based Optimization method

• URL: http://arxiv.org/abs/2605.03773v2
• Date: Mon, 11 May 2026 14:18:12 GMT
• Title: Computation of entanglement for quantum states by a Consensus-Based Optimization method
• Abstract summary: We propose a consensus-based optimization (CBO) method for entanglement computation.<n>To handle the variable interaction set, we introduce a mechanism allowing particles to exchange between different sizes.
• Score: 6.678834676966502
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The computation of quantum entanglement can be formulated as a high-dimensional nonconvex optimization problem with orthogonality constraints. In this work, we propose structure-preserving consensus-based optimization (CBO) methods for entanglement computation, with one approach based on a Hermitian formulation and the other evolving directly on the unitary manifold. To handle the variable dimension of the feasible set, we introduce a cross-dimensional interaction mechanism allowing exchange of information between particles of different sizes. Numerical experiments demonstrate that the proposed methods achieve accurate approximations.

Related papers

• Optimization-based Unfolding in High-Energy Physics [0.0]
  In High-Energy Physics, unfolding is the process of reconstructing true distributions of physical observables from detector-distorted measurements.<n>We develop a framework to tackle this problem using both classical and quantum-compatible methods.
  arXiv  Detail & Related papers  (2026-02-26T09:11:34Z)
• Multi-Dimensional Visual Data Recovery: Scale-Aware Tensor Modeling and Accelerated Randomized Computation [51.65236537605077]
  We propose a new type of network compression optimization technique, fully randomized tensor network compression (FCTN)<n>FCTN has significant advantages in correlation characterization and transpositional in algebra, and has notable achievements in multi-dimensional data processing and analysis.<n>We derive efficient algorithms with guarantees to solve the formulated models.
  arXiv  Detail & Related papers  (2026-02-13T14:56:37Z)
• Neural Optimal Transport Meets Multivariate Conformal Prediction [58.43397908730771]
  We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
  arXiv  Detail & Related papers  (2025-09-29T19:50:19Z)
• Numerical Optimization for Tensor Disentanglement [7.88541926763416]
  This paper focuses on tensor disentangling, the task of identifying transformations that reduce bond dimensions by exploiting gauge freedom in the network.<n>We formulate this problem as an optimization problem over orthogonal matrices acting on a single tensor's indices, aiming to minimize the rank of its matricized form.<n>To seek the often unknown optimal rank, we introduce a binary search strategy integrated with the disentangling procedure.
  arXiv  Detail & Related papers  (2025-08-26T20:17:48Z)
• Efficient Quantum Access Model for Sparse Structured Matrices using Linear Combination of Things [0.6138671548064355]
  We present a novel framework for Linear Combination of Unitaries (LCU)-style decomposition tailored to structured sparse matrices.<n>LCU is a foundational primitive in both variational and fault-tolerant quantum algorithms.<n>We introduce the Sigma basis, a compact set of simple, non-unitary operators that can better capture sparsity and structure.
  arXiv  Detail & Related papers  (2025-07-04T17:05:07Z)
• Multidimensional Adaptive Coefficient for Inference Trajectory Optimization in Flow and Diffusion [26.876236866996422]
  Flow and diffusion models have demonstrated strong performance and training stability across various tasks.<n>We propose the Multidimensional Adaptive Coefficient (MAC), a plug-in module for flow and diffusion models.
  arXiv  Detail & Related papers  (2024-04-22T13:20:01Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)
• Counting Phases and Faces Using Bayesian Thermodynamic Integration [77.34726150561087]
  We introduce a new approach to reconstruction of the thermodynamic functions and phase boundaries in two-parametric statistical mechanics systems. We use the proposed approach to accurately reconstruct the partition functions and phase diagrams of the Ising model and the exactly solvable non-equilibrium TASEP.
  arXiv  Detail & Related papers  (2022-05-18T17:11:23Z)
• Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents [102.42623636238399]
  We identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. We derive algorithms that exploit these geometric structures to solve these problems efficiently.
  arXiv  Detail & Related papers  (2022-03-20T16:23:17Z)
• Improving Metric Dimensionality Reduction with Distributed Topology [68.8204255655161]
  DIPOLE is a dimensionality-reduction post-processing step that corrects an initial embedding by minimizing a loss functional with both a local, metric term and a global, topological term. We observe that DIPOLE outperforms popular methods like UMAP, t-SNE, and Isomap on a number of popular datasets.
  arXiv  Detail & Related papers  (2021-06-14T17:19:44Z)
• Jointly Modeling and Clustering Tensors in High Dimensions [6.072664839782975]
  We consider the problem of jointly benchmarking and clustering of tensors. We propose an efficient high-maximization algorithm that converges geometrically to a neighborhood that is within statistical precision.
  arXiv  Detail & Related papers  (2021-04-15T21:06:16Z)
• Optimal Bayesian experimental design for subsurface flow problems [77.34726150561087]
  We propose a novel approach for development of chaos expansion (PCE) surrogate model for the design utility function. This novel technique enables the derivation of a reasonable quality response surface for the targeted objective function with a computational budget comparable to several single-point evaluations.
  arXiv  Detail & Related papers  (2020-08-10T09:42:59Z)
• Model Reduction and Neural Networks for Parametric PDEs [9.405458160620533]
  We develop a framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology.
  arXiv  Detail & Related papers  (2020-05-07T00:09:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.