Enrico Russo, Maurizio Palesi, Davide Patti et al.
Modular, distributed and multi-core architectures are currently considered a promising approach for scalability of quantum computing systems. The integration of multiple Quantum Processing Units necessitates classical and quantum-coherent communication, introducing challenges related to noise and quantum decoherence in quantum state transfers between cores. Optimizing communication becomes imperative, and the compilation and mapping of quantum circuits onto physical qubits must minimize state transfers while adhering to architectural constraints. The compilation process, inherently an NP-hard problem, demands extensive search times even with a small number of qubits to be solved to optimality. To address this challenge efficiently, we advocate for the utilization of heuristic mappers that can rapidly generate solutions. In this work, we propose a novel approach employing Deep Reinforcement Learning (DRL) methods to learn these heuristics for a specific multi-core architecture. Our DRL agent incorporates a Transformer encoder and Graph Neural Networks. It encodes quantum circuits using self-attention mechanisms and produce outputs through an attention-based pointer mechanism that directly signifies the probability of matching logical qubits with physical cores. This enables the selection of optimal cores for logical qubits efficiently. Experimental evaluations show that the proposed method can outperform baseline approaches in terms of reducing inter-core communications and minimizing online time-to-solution. This research contributes to the advancement of scalable quantum computing systems by introducing a novel learning-based heuristic approach for efficient quantum circuit compilation and mapping.