Existing schemes for synthesizing graph states in quantum networks are essentially edge-by-edge constructions, so quantities such as the time-slot depth and the resource overhead grow significantly with the edge density of the target graph. This paper proposes a new method. Exploiting the mathematical equivalence between joint Pauli-X measurements and graph pivot operations, we formulate graph state synthesis as a rank-2 reduction process of a difference matrix over GF(2), and give an upper bound floor(N/2) on the number of steps for synthesizing an arbitrary N-node graph state, independent of the edge density of the target graph state. At the physical level, the joint Pauli-X measurement of each step is mapped to a dual-star concurrent distribution. We model the protocol on Waxman physical topologies with fiber attenuation and give a heuristic algorithm, and evaluate it against a strengthened Steiner baseline through Monte Carlo experiments. The experimental results show that our protocol is superior in time-slot depth almost everywhere. The entanglement resource overhead, the total number of CZ gates, and the number of Pauli measurements drop below the baseline near edge density p approximately 0.3, and are superior across the board thereafter. The denser the target graph state, the more significant the advantage.
Existing schemes for synthesizing graph states in quantum networks are essentially edge-by-edge constructions, so quantities such as the time-slot depth and the resource overhead grow significantly with the edge density of the target graph. This paper proposes a new method. Exploiting the mathematical equivalence between joint Pauli-X measurements and graph pivot operations, we formulate graph state synthesis as a rank-2 reduction process of a difference matrix over GF(2), and give an upper bound floor(N/2) on the number of steps for synthesizing an arbitrary N-node graph state, independent of the edge density of the target graph state. At the physical level, the joint Pauli-X measurement of each step is mapped to a dual-star concurrent distribution. We model the protocol on Waxman physical topologies with fiber attenuation and give a heuristic algorithm, and evaluate it against a strengthened Steiner baseline through Monte Carlo experiments. The experimental results show that our protocol is superior in time-slot depth almost everywhere. The entanglement resource overhead, the total number of CZ gates, and the number of Pauli measurements drop below the baseline near edge density p approximately 0.3, and are superior across the board thereafter. The denser the target graph state, the more significant the advantage.
In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a given source graph state to a desired target graph state using only local operations. Recently it has been shown that deciding transformability is already NP-hard. In this paper, we present a CNF encoding for both local and non-local graph state operations, corresponding to one- and two-qubit Clifford gates and single-qubit Pauli measurements. We use this encoding in a bounded-model-checking set-up to synthesize the desired transformation. Additionally, for a completeness threshold on local transformations, we provide an upper bound on the length of the transformation if it exists. We evaluate the approach in two settings: the first is the synthesis of the ubiquitous GHZ state from a random graph state where we can vary the number of qubits, while the second is based on a proposed 14 node quantum network. We find that the approach is able to synthesize transformations for graphs up to 17 qubits in under 30 minutes.
Graph states are a class of important multiparty entangled quantum states, of which Bell pairs are the special case. Realizing a robust and fast distribution of arbitrary graph states in the downstream layer of the quantum network is essential for enabling large-scale quantum networks. To address this, we propose a novel quantum network protocol, called P2PGSD, inspired by the classical Peer-to-Peer network. This protocol efficiently implements general graph state distribution in the network layer, demonstrating significant advantages in resource efficiency and scalability, particularly for sparse graph states. An explicit mathematical model for the general graph state distribution problem has also been constructed, above which the intractability for a wide class of resource minimization problems is proved and the optimality of the existing algorithms is discussed. Moreover, we leverage the space-time quantum network for memory management in network challenges, drawing inspiration from special relativity. We suggest a universal quantum distributed computation framework to exploit the strengths of our protocols, as confirmed by numerical simulations that reveal up to a 50% enhancement for general sparse graph states. This work marks a significant step toward resource-efficient multiparty entanglement distribution for diverse network topologies.
We investigate the problem of compiling the generation of graph states to arbitrarily many distributed homogeneous quantum processing units (QPUs), providing a scalable partitioning algorithm and graph state generation protocol to minimize the number of Bell pairs required. Current approaches focus on the naive metric of cut edges to estimate the quantum communication cost. We show that the problem of balanced k graph partitioning, with the objective of minimizing the sizes of the maximum matchings between the partitions, leads to lower entanglement requirements across partitions. Our heuristic algorithm, BURY, partitions graph states to require fewer Bell pairs for generation than state-of-the-art k partition algorithms. Furthermore, we show that BURY reduces the cut-rank of the partitions, demonstrating that the partitioning found by our algorithm is likely to minimize the Bell pair utilization of any future improved distributed graph state generation protocol. We also discuss how our methods apply to the dynamic case where the graph state generation and measurement are performed concurrently. Our compilation approach provides a scalable foundation for reducing quantum network overhead for distributed measurement-based quantum computation (MBQC), as well as any scheme where distributed graph state generation is desired.
Graph states are a class of important multiparty entangled quantum states, of which Bell pairs are the special case. Realizing a robust and fast distribution of arbitrary graph states in the downstream layer of the quantum network is essential for enabling large-scale quantum networks. To address this, we propose a novel quantum network protocol, called P2PGSD, inspired by the classical Peer-to-Peer network. This protocol efficiently implements general graph state distribution in the network layer, demonstrating significant advantages in resource efficiency and scalability, particularly for sparse graph states. An explicit mathematical model for the general graph state distribution problem has also been constructed, above which the intractability for a wide class of resource minimization problems is proved and the optimality of the existing algorithms is discussed. Moreover, we leverage the space-time quantum network for memory management in network challenges, drawing inspiration from special relativity. We suggest a universal quantum distributed computation framework to exploit the strengths of our protocols, as confirmed by numerical simulations that reveal up to a 50% enhancement for general sparse graph states. This work marks a significant step toward resource-efficient multiparty entanglement distribution for diverse network topologies.
Graph states are a class of important multiparty entangled quantum states, of which Bell pairs are the special case. Realizing a robust and fast distribution of arbitrary graph states in the downstream layer of the quantum network is essential for enabling large-scale quantum networks. To address this, we propose a novel quantum network protocol, called P2PGSD, inspired by the classical Peer-to-Peer network. This protocol efficiently implements general graph state distribution in the network layer, demonstrating significant advantages in resource efficiency and scalability, particularly for sparse graph states. An explicit mathematical model for the general graph state distribution problem has also been constructed, above which the intractability for a wide class of resource minimization problems is proved and the optimality of the existing algorithms is discussed. Moreover, we leverage the space-time quantum network for memory management in network challenges, drawing inspiration from special relativity. We suggest a universal quantum distributed computation framework to exploit the strengths of our protocols, as confirmed by numerical simulations that reveal up to a 50% enhancement for general sparse graph states. This work marks a significant step toward resource-efficient multiparty entanglement distribution for diverse network topologies.
Photonic graph states with advanced topologies can enable measurement-based quantum computing, distributed quantum sensing, and quantum interconnects. However, the efficient generation of photonic graph states is limited by the probabilistic nature of photonic entangling operations and the exponential dependence of generation rate on resource cost. In this work, we study photonic graph state synthesis as a cost-aware decomposition problem, exploiting local Clifford (LC) equivalence to identify more synthesis-friendly representations of the target graph state before decomposition. Specifically, we propose Cost-aware Fusion-based Decomposition (CFD), a three-stage heuristic framework that decomposes a target graph state into ring, star, and linear motifs, and assembles them via Type-I fusion operations to minimize fusion overhead and physical-qubit consumption. We further show that selecting the LC-equivalent graph state with the minimum number of edges provides a highly effective proxy for near-optimal synthesis: in many cases it matches the best generation rate observed within the LC equivalence class under CFD, and in most remaining cases it remains close to it. Numerical evaluations on graph state orbit data and 2D and 3D lattice graph states demonstrate that CFD achieves up to 84.6\% reduction in resource overhead compared to baseline constructions, and yields improvements in photonic generation rate spanning multiple orders of magnitude. These results suggest that combining structure-aware motif decomposition with LC equivalence is a practical and scalable strategy for photonic graph state synthesis.