A 0.8395-approximation algorithm for the EPR problem

TL;DR

This paper presents a new approximation algorithm for the EPR problem with a ratio of 0.8395, utilizing novel bounds and refined quantum circuit parameterization, and discusses limitations of current methods.

Contribution

It introduces a novel nonlinear monogamy-of-entanglement bound and refined quantum circuit techniques for the EPR problem, achieving a better approximation ratio.

Findings

Achieved a 0.8395-approximation ratio for the EPR problem.

Proved limitations of current methods in surpassing this approximation ratio.

Identified the need for fundamentally new techniques for further improvements.

Abstract

We give an efficient 0.8395-approximation algorithm for the EPR Hamiltonian. Our improvement comes from a new nonlinear monogamy-of-entanglement bound on star graphs and a refined parameterization of a shallow quantum circuit from previous works. We also prove limitations showing that current methods cannot achieve substantially better approximation ratios, indicating that further progress will require fundamentally new techniques.