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

TL;DR

This paper introduces structure-preserving consensus-based optimization methods to compute quantum entanglement, effectively handling high-dimensional, nonconvex problems with orthogonality constraints.

Contribution

It presents novel CBO algorithms tailored for entanglement computation, including a Hermitian approach and a unitary manifold approach, with a mechanism for cross-dimensional information exchange.

Findings

Methods achieve accurate entanglement approximations

Algorithms effectively handle high-dimensional, nonconvex problems

Cross-dimensional interaction improves optimization performance

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.