基于秩-2 GF(2)归约的量子网络中任意图态的分布式合成
Distributed synthesis of arbitrary graph states in quantum networks via rank-two GF(2) reduction
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中文总结 AI 辅助
该研究提出一种基于GF(2)秩-2归约的量子网络图态分布式合成协议，将步骤数上界与边密度解耦，实验表明其在时隙深度、资源开销上均优于基线，边越密优势越明显。
中文摘要 AI 辅助
现有量子网络中图态合成方案本质为逐边构造，因此时隙深度、资源开销等指标会随目标图的边密度显著增长。本文提出一种新方法：利用联合泡利X测量与图枢轴操作的数学等价性，将图态合成形式化为GF(2)上差矩阵的秩-2归约过程，给出合成任意N节点图态的步骤数上界为floor(N/2)，且该上界与目标图态的边密度无关。物理层面，每一步的联合泡利X测量被映射为双星型并发分布。我们在含光纤损耗的Waxman物理拓扑上对协议建模并设计启发式算法，通过蒙特卡洛实验与增强型Steiner基线对比评估。实验结果显示，本协议在几乎所有场景的时隙深度上均优于基线；当边密度p约为0.3时，纠缠资源开销、CZ门总数及泡利测量次数均低于基线，且边密度高于0.3后优势全面体现，目标图态越密，优势越显著。
英文摘要
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.
