As quantum computers require highly specialized and stable environments to operate, expanding their capabilities within a single system presents significant technical challenges. By interconnecting multiple quantum processors, distributed quantum computing can facilitate the execution of more complex and larger-scale quantum algorithms. End-to-end heuristics for the distribution of quantum circuits have been developed so far. In this work, we derive an exact integer programming approach for the Distributed Quantum Circuit (DQC) problem, assuming fixed module allocations. Since every DQC algorithm necessarily yields a module allocation function, our formulation can be integrated with it as a post-processing step. This improves on the hypergraph partitioning formulation, which finds a module allocation function and an efficient distribution at once. We also show that a suboptimal heuristic to find good allocations can outperform previous methods. In particular, for quantum Fourier transform circuits, we conjecture from experiments that the optimal module allocation is the trivial one found by this method.

翻译：由于量子计算机需要在高度专业化和稳定的环境中运行，在单一系统内扩展其能力面临着巨大的技术挑战。通过互连多个量子处理器，分布式量子计算能够促进更复杂、更大规模量子算法的执行。迄今为止，已开发出用于量子电路分布的端到端启发式方法。在本工作中，我们针对分布式量子电路（DQC）问题推导出一种精确的整数规划方法，该方法假设模块分配是固定的。由于每个DQC算法必然会产生一个模块分配函数，我们的公式可以将其作为后处理步骤与之集成。这改进了超图划分公式，后者需要同时找到模块分配函数和高效的分布方案。我们还证明，用于寻找良好分配的次优启发式方法可以超越先前的方法。特别地，对于量子傅里叶变换电路，我们根据实验推测，最优的模块分配正是该方法所发现的平凡解。