Optimized Distribution of Entanglement Graph States in Quantum Networks

TL;DR

This work tackles the problem of optimally distributing multipartite entanglement graph states across quantum networks by modeling graph-state generation as a level-based flow problem. It introduces a hypergraph-based linear programming framework that accounts for the stochastic success of fusion operations and network heterogeneity, yielding provably optimal generation schemes for path and tree graph states and adaptable strategies for broader graph classes. By deriving both exact (path/tree) and computationally efficient (distance-based, left/right-sided, two-stage/one-stage) LP formulations, the approach balances optimality and scalability. NetSquid simulations demonstrate up to orders-of-magnitude improvements over prior methods while maintaining high fidelity, underscoring the framework’s potential for enabling large-scale, robust quantum networks.

Abstract

Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum Networks (QNs) can help address this challenge by enabling the construction of large, robust, and more capable quantum computing platforms by connecting smaller quantum computers. Moreover, unlike classical systems, QNs can enable fully secured long-distance communication. Thus, quantum networks lie at the heart of the success of future quantum information technologies. In quantum networks, multipartite entangled states distributed over the network help implement and support many quantum network applications for communications, sensing, and computing. Our work focuses on developing optimal techniques to generate and distribute multipartite entanglement states efficiently. Prior works on generating general multipartite entanglement states have focused on the objective of minimizing the number of maximally entangled pairs (EPs) while ignoring the heterogeneity of the network nodes and links as well as the stochastic nature of underlying processes. In this work, we develop a hypergraph based linear programming framework that delivers optimal (under certain assumptions) generation schemes for general multipartite entanglement represented by graph states, under the network resources, decoherence, and fidelity constraints, while considering the stochasticity of the underlying processes. We illustrate our technique by developing generation schemes for the special cases of path and tree graph states, and discuss optimized generation schemes for more general classes of graph states. Using extensive simulations over a quantum network simulator (NetSquid), we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude.

Figures (20)

• Figure 1: A swapping tree over a path. The leaves of the tree are the link EPs, which are being generated continuously. Here, the notation $(x_i, x_j)$ represents an EP over two qubits residing in the network nodes $x_i$ and $x_j$.
• Figure 2: (a) A quantum network with 7 nodes $\{x_1, x_2, \ldots, x_7\}$, (b) Graph State $G$ with 4 vertices named 1 to 4, and (c) Distributed Graph State (in red) for the graph state $G$ with $\tau(1) = x_2, \tau(2) = x_4, \tau(3)=x_5, \tau(4)=x_7$.
• Figure 3: Local operations used in our fusion operations.
• Figure 4: Level-based structure. The above structure is an "aggregation" of two fusion trees. The leaf node $a$'s generation rate of 36 units is "split" into 9 and 27 for the two different (red and blue) fusion operations. The root node represents the final/target graph state formed in two different ways---for a total generation rate of 6 (3 from each fusion operation). We assume that a parent's generation rate is 1/3 of the rate of its children/operands (which are equal).
• Figure 5: A potential solution (not necessarily optimal), a level-based structure, for the network graph and distributed graph state in Fig. \ref{['fig:graphs']}. The distributed graph state corresponding to a node in the structure is represented by the actual graph and its distribution (e.g., $x_2$---$x_4$ represents an edge graph state distributed over nodes $x_2$ and $x_4)$.

Theorems & Definitions (4)

• Definition 1
• Theorem 1
• Theorem 2
• Theorem 3