Modular and networked quantum architectures can scale beyond the qubit count of a single device, but executing a circuit across modules requires implementing non-local two-qubit gates using shared entanglement (ebits) and classical communication, making ebit cost a central resource in distributed execution. The resulting distributed quantum circuit (DQC) problem is combinatorial, motivating prior heuristic approaches such as hypergraph partitioning. In this work, we decouple module allocation from distribution. For a fixed module allocation (i.e., assignment of each qubit to a specific Quantum Processing Unit), we formulate the remaining distribution layer as an exact binary integer programming (BIP). This yields solver-optimal distributions for the fixed-allocation subproblem and can be used as a post-processing step on top of any existing allocation method. We derive compact BIP formulations for four or more modules and a tighter specialization for three modules. Across a diverse benchmark suite, BIP post-processing reduces ebit cost by up to 20\% for random circuits and by more than an order of magnitude for some arithmetic circuits. While the method incurs offline classical overhead, it is amortized when circuits are executed repeatedly.

翻译：模块化与网络化量子架构能够突破单一设备的量子比特数量限制，但跨模块执行电路需利用共享纠缠（ebit）与经典通信实现非局域双量子比特门，这使得纠缠比特成本成为分布式执行的核心资源。由此产生的分布式量子电路（DQC）问题具有组合复杂性，催生了先前基于超图分割等启发式方法的研究。本工作中，我们将模块分配与分布过程解耦。针对固定的模块分配（即每个量子比特被指定到特定量子处理单元的情形），我们将剩余分布层建模为精确的二进制整数规划（BIP）问题。该方法可为固定分配子问题提供求解器最优的分布方案，并可作为后处理步骤应用于任何现有分配方法之上。我们推导了适用于四个及以上模块的紧凑型BIP公式，并针对三模块情形提出了更紧凑的专用公式。在多样化基准测试中，BIP后处理使随机电路的纠缠比特成本降低高达20%，对某些算术电路更可实现超过一个数量级的优化。虽然该方法会产生离线经典计算开销，但在电路重复执行时可实现开销分摊。