Optimized Distribution of Entanglement Graph States in Quantum Networks (2405.00222v2)

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.

• The paper presents a hypergraph-based linear programming framework that optimizes the generation and distribution of multipartite entangled graph states.
• Simulations demonstrate up to 100x improvement in generation rates and high fidelity across diverse network conditions.
• The approach efficiently manages resource constraints, stochastic quantum processes, and decoherence, paving the way for scalable quantum networks.

Optimized Distribution of Entanglement Graph States in Quantum Networks

This paper presents an innovative framework aimed at optimizing the distribution and generation of multipartite entangled graph states in quantum networks. The authors provide a comprehensive linear programming approach to achieve efficient entanglement distribution, accounting for network resource constraints, the stochastic nature of underlying quantum processes, and decoherence. Their results are substantiated through extensive simulations which highlight significant improvements over existing methods.

Context and Objectives

Quantum networks (QNs) offer the potential to interconnect smaller quantum computers to form robust, large-scale quantum computing platforms. These networks facilitate various applications, including secure communication, sensing, and quantum computing, by enabling the distribution of multipartite entangled states. Traditional approaches to generating these states have primarily focused on bipartite or Greenberger-Horne-Zeilinger (GHZ) states and often neglect the heterogeneity of network resources and the stochastic nature of entanglement generation.

The primary objective of this work is to develop provably optimal techniques for generating and distributing multipartite entangled states, specifically graph states, under realistic network conditions. The authors propose a hypergraph-based linear programming framework that seeks to maximize the expected generation rate of graph states, considering network heterogeneity, resource constraints, and decoherence.

Methodology

The framework involves constructing hypergraphs that represent all potential intermediate states and fusion operations for generating the desired graph states. The key elements of the approach include:

1. Notation and Intermediate States: The authors introduce a notation system for intermediate graph states. For instance, in the case of path graph states, intermediate states are represented as connected subgraphs augmented with edges at both ends.
2. Fusion Operations: Two types of fusion operations are employed—fusion-retain and fusion-discard—that merge smaller graph states to progressively build larger ones. These operations are represented as hyperedges in the constructed hypergraph.
3. Hypergraph and Linear Programming Formulation: The hypergraph's vertices represent potential intermediate states, while the hyperedges denote fusion operations. The linear programming formulation includes capacity constraints (to ensure resource limitations are respected) and flow constraints (to maintain consistency in the generation rates across the hypergraph). The objective is to maximize the sum of the generation rates of the target graph state.
4. Computational Efficiency: Recognizing the potential computational overhead of solving large linear programs, the authors propose approximation schemes that limit the number of intermediate states considered. These schemes, such as distance-based LPs and two-stage approaches, provide computationally feasible solutions without significantly compromising optimality.

Results

Extensive simulations using the NetSquid simulator demonstrate the efficacy of the proposed techniques. Key findings include:

• Improved Generation Rates: The proposed methods outperform prior schemes by up to several orders of magnitude. For example, generation rates for path and tree graph states show improvements of up to 100 times and even more.
• High Fidelity: The generated graph states maintain high fidelity, crucial for practical applications. The stochastic nature of fusion operations and decoherence are effectively managed within the proposed LP framework.
• Scalability: The approaches scale efficiently with both network size and the complexity of the target graph state. The approximation schemes in particular offer a balance between computational feasibility and optimal performance.

Implications and Future Directions

This work signifies a substantial advancement in the domain of quantum network entanglement distribution. The implications are manifold:

• Practical Deployment: The proposed framework provides a pathway toward the practical deployment of large-scale QNs by facilitating efficient entanglement distribution.
• Enhanced Capabilities: By optimizing resource usage and considering the inherent stochasticity of quantum processes, the framework enhances the capabilities of quantum networks in terms of reliability and performance.
• Future Research: The framework's versatility suggests that it could be extended to other classes of graph states and potentially adapted for concurrent generation of multiple graph states. Further research could explore reducing the assumptions and extending the methods to broader and more complex quantum network scenarios.

Conclusion

The paper presents a rigorous and effective approach to optimizing the distribution of entangled graph states in quantum networks. The combination of a hypergraph-based representation and linear programming offers a powerful tool for addressing the challenges of entanglement distribution in realistic quantum networks, paving the way for future advancements in quantum information processing.