A 0.8395-approximation algorithm for the EPR problem

2025-12-10

AI Summary

This work addresses the quantum constraint satisfaction problem (qCSP) induced by the EPR Hamiltonian, aiming to improve the approximation ratio of near-term quantum algorithms. We derive the first nonlinear monogamy-of-entanglement bound for star graphs, overcoming fundamental limitations of conventional linear monogamy constraints. Leveraging this bound, we redesign the parameterization structure of shallow variational quantum circuits—integrating entanglement analysis, nonlinear inequality derivation, and circuit architecture optimization. Experimentally, our approach achieves an approximation ratio of 0.8395 on the EPR qCSP, establishing the current state-of-the-art. Moreover, we rigorously prove that all existing frameworks relying on linear monogamy are provably capped at 0.8402, thereby exposing an inherent barrier and underscoring the necessity of nonlinear entanglement characterization and novel circuit design principles for further progress.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Non-convex Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• Develops a 0.8395-approximation algorithm for the EPR Hamiltonian
• Introduces a new nonlinear monogamy-of-entanglement bound for star graphs
• Proves limitations of current methods for achieving better approximation ratios

Innovation

• New monogamy-of-entanglement bound on star graphs
• Refined parameterization of shallow quantum circuits
• Limitations proof for current approximation methods