The practical realization of quantum programs that require large-scale qubit systems is hindered by current technological limitations. Distributed Quantum Computing (DQC) presents a viable path to scalability by interconnecting multiple Quantum Processing Units (QPUs) through quantum links, facilitating the distributed execution of quantum circuits. In DQC, EPR pairs are generated and shared between distant QPUs, which enables quantum teleportation and facilitates the seamless execution of circuits. A primary obstacle in DQC is the efficient mapping and routing of logical qubits to physical qubits across different QPUs, necessitating sophisticated strategies to overcome hardware constraints and optimize communication. We introduce a novel compiler that, unlike existing approaches, prioritizes reducing the expected execution time by jointly managing the generation and routing of EPR pairs, scheduling remote operations, and injecting SWAP gates to facilitate the execution of local gates. We present a real-time, adaptive approach to compiler design, accounting for the stochastic nature of entanglement generation and the operational demands of quantum circuits. Our contributions are twofold: (i) we model the optimal compiler for DQC using a Markov Decision Process (MDP) formulation, establishing the existence of an optimal algorithm, and (ii) we introduce a constrained Reinforcement Learning (RL) method to approximate this optimal compiler, tailored to the complexities of DQC environments. Our simulations demonstrate that Double Deep Q-Networks (DDQNs) are effective in learning policies that minimize the depth of the compiled circuit, leading to a lower expected execution time and likelihood of successful operation before qubits decohere.

翻译：实现需要大规模量子比特系统的量子程序面临着当前技术局限性的阻碍。分布式量子计算（DQC）通过量子链路互连多个量子处理单元（QPU），为可扩展性提供了一条可行路径，促进了量子电路的分布式执行。在DQC中，EPR对在远距离QPU之间生成并共享，这实现了量子隐形传态并促进了电路的无缝执行。DQC的一个主要障碍是跨不同QPU的逻辑量子比特到物理量子比特的高效映射与路由，这需要复杂的策略来克服硬件约束并优化通信。我们提出了一种新型编译器，与现有方法不同，它通过联合管理EPR对的生成与路由、调度远程操作以及插入SWAP门以促进局部门执行，优先减少预期执行时间。我们提出了一种实时自适应的编译器设计方法，考虑了纠缠生成的随机性以及量子电路的操作需求。我们的贡献有两方面：(i) 我们使用马尔可夫决策过程（MDP）形式化建模了DQC的最优编译器，确立了最优算法的存在性；(ii) 我们引入了一种约束强化学习（RL）方法来近似这种最优编译器，使其适应DQC环境的复杂性。我们的仿真表明，双深度Q网络（DDQNs）在学习最小化编译电路深度的策略方面是有效的，从而在量子比特退相干前降低了预期执行时间并提高了操作成功概率。