  Quantum computing represents a paradigm shift in computation, offering the
potential to solve complex problems intractable for classical computers.
Although current quantum processors already consist of a few hundred of qubits,
their scalability remains a significant challenge. Modular quantum computing
architectures have emerged as a promising approach to scale up quantum
computing systems. This paper delves into the critical aspects of distributed
multi-core quantum computing, focusing on quantum circuit mapping, a
fundamental task to successfully execute quantum algorithms across cores while
minimizing inter-core communications. We derive the theoretical bounds on the
number of non-local communications needed for random quantum circuits and
introduce the Hungarian Qubit Assignment (HQA) algorithm, a multi-core mapping
algorithm designed to optimize qubit assignments to cores with the aim of
reducing inter-core communications. Our exhaustive evaluation of HQA against
state-of-the-art circuit mapping algorithms for modular architectures reveals a
$4.9\times$ and $1.6\times$ improvement in terms of execution time and
non-local communications, respectively, compared to the best performing
algorithm. HQA emerges as a very promising scalable approach for mapping
quantum circuits into multi-core architectures, positioning it as a valuable
tool for harnessing the potential of quantum computing at scale.
