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International Conference on Advanced Communications Technology (ICACT)

Distribution and Segmentation Methods of Graph States Based on Quantum Networks

Haomin Chen, Tianze Zhu, G. Yu, Yiling Lin, Xiaofeng Jiang

Published Feb 16, 2025• 1 citation
Publisher

Abstract

In recent years, quantum communication and quantum computing have become strategic technologies of great importance to countries around the world, with profound implications for individuals, businesses, and even nations. Among these, graph states are a very important class of multi-particle entangled states, playing a crucial role in fields such as quantum secret sharing, measurement-based quantum computing, and quantum metrology. However, the distribution of graph states faces the following challenges: existing quantum communication networks designed for single-qubit transmission cannot effectively accomplish graph state distribution tasks, and current methods for graph state distribution lack consideration of node resources, making it difficult to complete graph state distribution in some cases.We conduct research on cross-node graph states distribution methods in quantum communication networks under limited resource constraints. To address the issue that current quantum communication networks cannot handle graph states and other multi-particle entangled states, a graph state distribution method is proposed. This method combines local operations and classical communication to meet the distribution requirements for graph states, which are multi-particle entangled states. Additionally, to solve the problem of limited quantum resources at individual nodes, we proposed a graph states segmentation method. This method divides a complete graph state into subgraphs for distribution and subsequently integrates them, enabling graph state distribution services in a broader range of resource scenarios.

DOI
10.23919/icact63878.2025.10936711

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In recent years, quantum communication and quantum computing have become strategic technologies of great importance to countries around the world, with profound implications for individuals, businesses, and even nations. Among these, graph states are a very important class of multi-particle entangled states, playing a crucial role in fields such as quantum secret sharing, measurement-based quantum computing, and quantum metrology. However, the distribution of graph states faces the following challenges: existing quantum communication networks designed for single-qubit transmission cannot effectively accomplish graph state distribution tasks, and current methods for graph state distribution lack consideration of node resources, making it difficult to complete graph state distribution in some cases.We conduct research on cross-node graph states distribution methods in quantum communication networks under limited resource constraints. To address the issue that current quantum communication networks cannot handle graph states and other multi-particle entangled states, a graph state distribution method is proposed. This method combines local operations and classical communication to meet the distribution requirements for graph states, which are multi-particle entangled states. Additionally, to solve the problem of limited quantum resources at individual nodes, we proposed a graph states segmentation method. This method divides a complete graph state into subgraphs for distribution and subsequently integrates them, enabling graph state distribution services in a broader range of resource scenarios.
Abstract Multi-particle entanglement state distribution is a crucial component for executing the quantum communication or computation protocols over quantum networks, and the graph state is an important class of multi-particle entanglement states. If the graph states can be efficiently distributed over quantum networks, the execution costs of the quantum communication or computation protocols will be greatly improved. Therefore, this study proposes an enhanced graph state transfer algorithm, which is used to distribute the graph state across a quantum network to reduce the required number of qubit measurements, quantum operation implementation, and qubit consumption without adding any additional quantum device.
Graph states are a particular class of entangled quantum states, that play essential roles in distributed quantum computing and quantum communication. In both cases, graph states are usually used as resources for a specific set of quantum computers to share information. Therefore, distributing a graph state across a quantum network is an important problem. Currently, we do not have an efficient method for generating Einstein-Podolsky-Rosen(EPR) pairs on demand. Hence EPR pairs needed to distribute graph states are critical resources, and it is important to design distribution algorithms that reduce the need for such resources. Meignant et al. [1] presented the edge-decorated complete graph algorithm that uses n(n – 1)/2 number of EPR pairs to distribute the given graph state, where n is number of node in the network. Fischer et al [2] proposed the Graph State Transfer (GST) algorithm, which consumes fewer EPR pairs. However, GST requires an unbounded amount of memory at each node and preparation of the entire graph state in a single network node. In this poster, we present an integer programming formulation that removes these two assumptions. The model accounts for both the topology of the quantum network and memory constraints at each network node. Meanwhile, we propose a greedy algorithm to solve the problem.
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.
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 bya\boldsymbol{a}asystem 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.
Graph states form an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes—quantum computers within which local operations are free—and EPR pairs shared between nodes that can continually be generated. We prove upper bounds for our approach on the number of EPR pairs consumed, completion time, and amount of classical communication required, all of which are equal to or better than that of prior work [10]. We also reduce the problem of minimizing the completion time to distribute a graph state using our approach to a network flow problem having polynomial time complexity.
Quantum graph state is a special class of nonlocal state among multiple quantum particles, underpinning several nonclassical and promising applications such as quantum computing and quantum secret sharing. Recently, establishing quantum graph states among physically distant nodes has gained increasing popularity owing to its potential in expanding current quantum applications in scale. Existing research on this topic relies on a two-step approach: first distributing low-dimension elementary entanglement to target nodes, and then fusing them into a high-dimension quantum graph state. However, most existing studies focus solely on minimizing costs (e.g., the number of elementary entanglements consumed) to entangle target nodes, while neglecting the structure of the final quantum graph state. This can easily result in weak system entanglement, jeopardizing the graph state under partial measurement or noises. In this paper, we aim to establish any arbitrary quantum graph states of strong entanglement structures at a much lower cost than the state of the art. The method is to search for and establish an alternative state to the target state that is of lowest cost in creation. Subsequently, we transform such an alternative state back to the target state via compressed single-qubit Clifford operations. To verify the performance of our developed algorithm, we conduct comprehensive simulations based on an open dataset containing all graph state structures up to 8 qubits. The results demonstrate fast algorithm convergence, an increased success probability in distributing any graph states, and 53.57%53.57\%53.57% saving in ERP cost compared with the state-of-the-art baseline.