Near-Optimal Techniques for Distributed Entanglement Generation and Purification

We address the problem of efficiently distributing high-fidelity entangled states across the nodes of a quantum network—a fundamental requirement for quantum communication, distributed quantum computing, and emerging quantum internet applications. We consider a repeater-based architecture that combines entanglement swapping (or fusion) with purification operations, which enhance fidelity by consuming additional entangled pairs. While prior work has explored routing and limited purification strategies, we present the first algorithms for fidelity-constrained entanglement distribution that are near-optimal and compatible with arbitrary purification models. Our approach introduces the notion of purification-augmented entanglement trees, and we develop dynamic programming (DP) algorithms to construct such trees that maximize the generation rate of entangled pairs (EPs) under fidelity constraints. We further extend our framework to a linear programming (LP)–based flow model that enables simultaneous generation of EPs across multiple source-destination pairs. For multipartite entanglement, we generalize our methods to GHZ and arbitrary graph states, supported by novel analytical models for fidelity evolution under fusion and purification. We evaluate our techniques using the NetSquid quantum network simulator and observe consistent performance improvements over prior approaches—achieving an average 50\% increase in generation rate, and up to 100-150\% in some scenarios.