Title: Compiler for Distributed Quantum Computing: a Reinforcement Learning Approach

Abstract: 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.