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

arXiv (Cornell University)

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.

Authors 3

1. Michaël Herty Aachen Chair in Numerical Analysis

   RWTH Aachen University

   Affiliation as printed

   Chair in Numerical Analysis , IGPM , RWTH Aachen University , Im Süsterfeld 2 , D-52072 Aachen , Germany

2. Yijia Tang

   Karlsruhe Institute of Technology · University of Pretoria

   Affiliation as printed

   Department of Mathe- matics and Applied Mathematics , University of Pretoria , Private Bag X20 , Hatfield 0028 , South Africa Corresponding author ,

   Scientific Computing Center , Karlsruhe Institute of Technology , 76131 Karlsruhe , Germany

3. Yizhou Zhou Aachen

   RWTH Aachen University

   Affiliation as printed

   IGPM , RWTH Aachen University , Im Süsterfeld 2 , D-52072 Aachen , Germany