通过因子图范式实现可扩展的分布式量子优化框架
A Scalable Distributed Quantum Optimization Framework via Factor Graph Paradigm
AI总结：
本文提出一种结构感知的分布式量子优化框架，通过因子图建模和松散耦合子问题协调，实现Grover-like的查询复杂度和资源优化。
摘要：
分布式量子计算（DQC）将许多小型量子处理器连接成一台逻辑机器，为实现可扩展的量子计算提供了一条实用路线。然而，大多数现有的DQC范式都是结构无关的。Peng等人在[Phys. Rev. Lett., 2020年10月]提出的电路切割方法以牺牲指数级的经典后处理为代价减少每个设备的量子比特数量，而Avron等人在[Phys. Rev. A., 2021年11月]提出的搜索空间划分方法虽然将工作负载分布开，但削弱了Grover理想的二次加速效果。在本文中，我们引入了一个结构感知的分布式量子优化框架，解决了复杂性-资源权衡的问题。我们将目标函数建模为因子图，并暴露其稀疏相互作用结构。我们沿着其自然的``缝线''，即边界变量的分割器，切割图以获得松散耦合的子问题，这些子问题可以适应资源受限的处理器。我们通过共享纠缠协调这些子问题，使网络执行单一的全局相干搜索，而不是独立的局部搜索。我们证明了这种设计保持了Grover-like的扩展性：对于大小为N的搜索空间，我们的框架在处理器和分割因子依赖下实现O(√N)的查询复杂度，同时放松了每个处理器的量子比特要求。我们通过分层的分治策略扩展了该框架，使其能够扩展到大规模优化问题，并支持两种操作模式：一种是用于容错网络的完全相干模式，另一种是在近期设备上插入测量以限制电路深度的混合模式。我们通过在多种网络拓扑上进行的模拟验证了预测的查询-纠缠权衡，并展示了结构感知分解为量子网络上的可扩展分布式量子优化提供了实际路径。
英文摘要：
Distributed quantum computing (DQC) connects many small quantum processors into a single logical machine, offering a practical route to scalable quantum computation. However, most existing DQC paradigms are structure-agnostic. Circuit cutting proposed by Peng et al. in [Phys. Rev. Lett., Oct. 2020] reduces per-device qubits at the cost of exponential classical post-processing, while search-space partitioning proposed by Avron et al. in [Phys. Rev. A., Nov. 2021] distributes the workload but weakens Grover's ideal quadratic speedup. In this paper, we introduce a structure-aware framework for distributed quantum optimization that resolves this complexity-resource trade-off. We model the objective function as a factor graph and expose its sparse interaction structure. We cut the graph along its natural ``seams'', i.e., a separator of boundary variables, to obtain loosely coupled subproblems that fit on resource-constrained processors. We coordinate these subproblems with shared entanglement, so the network executes a single globally coherent search rather than independent local searches. We prove that this design preserves Grover-like scaling: for a search space of size $N$, our framework achieves $O(\sqrt{N})$ query complexity up to processors and separator dependent factors, while relaxing the qubit requirement of each processor. We extend the framework with a hierarchical divide-and-conquer strategy that scales to large-scale optimization problems and supports two operating modes: a fully coherent mode for fault-tolerant networks and a hybrid mode that inserts measurements to cap circuit depth on near-term devices. We validate the predicted query-entanglement trade-offs through simulations over diverse network topologies, and we show that structure-aware decomposition delivers a practical path to scalable distributed quantum optimization on quantum networks.
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