Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum networks 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, quantum networks 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 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, we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude.
Building large-scale quantum computers, essential to demonstrating quantum advantage, is a key challenge. Quantum networks 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, quantum networks 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 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, we demonstrate the effectiveness of our developed techniques and show that they outperform prior known schemes by up to orders of magnitude.
Quantum networks are important for quantum communication and consist of entangled states that are essential for many tasks such as quantum teleportation, quantum key distribution, quantum sensing and quantum error correction. Graph states are a specific class of multipartite entangled states that can be represented by graphs. We propose a novel approach for distributing graph states across a quantum network. We show that the distribution of graph states can be characterised byasystem of subgraph complementations, which we also relate to the minimum rank of the underlying graph and the degree of entanglement quantified by the Schmidt-rank of the quantum state. We analyse resource usage for our algorithm and show it to match or be improved in the number of qubits, bits for classical communication and EPR pairs utilised, as compared to prior work. The number of local operations is efficient, and the resource consumption for our approach scales linearly in the number of vertices. This presents a quadratic improvement in completion time for several classes of graph states represented by dense graphs, and implies a potential for improved fidelity in the presence of noise. Common classes of graph states are classified along with the optimal time for their distribution using subgraph complementations. We also provide a framework to similarly find the optimal sequence of operations to distribute an arbitrary graph state, and prove upper bounds along with providing approximate greedy algorithms.
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite entangled states that can be represented by graphs. We propose a novel approach for distributing graph states across a quantum network. We show that the distribution of graph states can be characterized by a system of subgraph complementations, which we also relate to the minimum rank of the underlying graph and the degree of entanglement quantified by the Schmidt-rank of the quantum state. We analyze resource usage for our algorithm and show that it improves on the number of qubits, bits for classical communication, and EPR pairs utilized, as compared to prior work. In fact, the number of local operations and resource consumption for our approach scales linearly in the number of vertices. This produces a quadratic improvement in completion time for several classes of graph states represented by dense graphs, which translates into an exponential improvement by allowing parallelization of gate operations. This leads to improved fidelities in the presence of noisy operations, as we show through simulation in the presence of noisy operations. We classify common classes of graph states, along with their optimal distribution time using subgraph complementations. We find a sequence of subgraph complementation operations to distribute an arbitrary graph state which we conjecture is close to the optimal sequence, and establish upper bounds on distribution time along with providing approximate greedy algorithms.
We introduce a repeater scheme to efficiently distribute multipartite entangled states in a quantum network with optimal scaling. The scheme allows to generate graph states such as 2D and 3D cluster states of growing size or GHZ states over arbitrary distances, with a constant overhead per node/channel that is independent of the distance. The approach is genuine multipartite, and is based on the measurement-based implementation of multipartite hashing, an entanglement purification protocol that operates on a large ensemble together with local merging/connection of elementary building blocks. We analyze the performance of the scheme in a setting where local or global storage is limited, and compare it to bipartite and hybrid approaches that are based on the distribution of entangled pairs. We find that the multipartite approach offers a storage advantage, which results in higher efficiency and better performance in certain parameter regimes. We generalize our approach to arbitrary network topologies and different target graph states.
Large-scale quantum networks depend on the efficient distribution of entangled pairs between distant nodes. However, state-of-the-art solutions rely on restrictive operational assumptions, incur prohibitive computational complexity, and optimize metrics misaligned with application needs. This paper addresses the entanglement distribution problem introducing four pivotal advances. First, since the primary application of quantum communication is private information transmission, we derive the Ensemble Capacity, a novel metric that quantifies the private classical information enabled by entanglement distribution. Second, we propose a generalized formulation of the Entanglement Distribution Problem that allows arbitrary sequencing of entanglement swapping and purification, removing the structural restrictions of prior models. Third, to navigate the resulting combinatorial space, we introduce a dynamic programming-based hypergraph generation algorithm that preserves exact, continuous fidelities, avoiding quantization, while pruning sub-optimal sequences in advance. Finally, we integrate these solutions into CODE, a two-tier orchestration framework enabling near-real-time network operation. Extensive evaluations show that our approach achieves higher private information capacity and significantly lower computational complexity than existing solutions, while meeting the sub-second latency requirements of dynamic quantum network operation.
In quantum networks, multipartite entangled states distributed over the network are useful in implementing and supporting many quantum network applications for communications, sensing, and computing. The focus of our work is to de-velop techniques to efficiently generate distributed Greenberger-Horne-Zeilinger (GHZ) states, a special class of multipartite entanglement states. Prior works on generating GHZ states have focused on the objective of minimizing the number of maximally entangled (bipartite) pairs (EPs), while ignoring the stochastic nature of quantum processes and assuming uniform network links for generating EPs. In contrast, in our work, we take into consideration the stochastic nature of quantum networks, and focus on maximizing the expected generated rate of the GHZ states under given fidelity constraints. In this context, we develop two efficient generation schemes, viz., Fusion - Retain - only and General Fusion, comprised of optimal or near-optimal sub-steps. Both schemes, at a high-level, first determine a way to “connect” the nodes over which the GHZ state is to distributed, and then, determine a sequence of fusion operations on the EPs created over the connections. Using extensive simulations over a quantum network simulator (NetSquid), we demonstrate the effectiveness of our developed techniques and show that our schemes outperform prior work as well as a simple centralized approach by up to orders of magnitude while generating GHZ states of tolerable fidelity.
The effective routing of entanglement over a quantum network is a fundamental problem in quantum communication. The distribution and reshaping of multipartite entanglement over a quantum network requires scalable protocols that adapt to the underlying topology. Graph states provide a convenient framework for this challenging task, as they encode global entanglement in a structured way that can be locally manipulated to produce a variety of target states, without requiring additional long-distance quantum operations. In this article, we propose graph-state-based routing protocols for sharing GHZ states, achieving larger sizes than those achieved in the existing works for given network topologies. For this improvement, we consider tree structures connecting the users participating in the final GHZ states, as opposed to the linear configurations used in the earlier works. In particular, for grid networks, we show special constructions of such trees that achieve larger GHZ states than the prior works. Moreover, if the user nodes along which the entanglement is to be routed are pre-specified, a strategy is proposed to accomplish this routing.