  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.
