This paper explores the challenges and solutions in mapping quantum circuits onto multi-core quantum computing architectures, focusing on minimizing non-local communications. It introduces the Hungarian Qubit Assignment (HQA) algorithm, which optimizes qubit assignments to cores to reduce inter-core communications. The paper derives theoretical bounds on the number of non-local communications for random quantum circuits and evaluates HQA against state-of-the-art mapping algorithms. The results show that HQA improves execution time and reduces non-local communications by 4.9× and 1.6×, respectively, compared to the best-performing algorithm. The paper highlights the potential of HQA as a scalable approach for mapping quantum circuits into multi-core architectures, positioning it as a valuable tool for advancing quantum computing at scale.This paper explores the challenges and solutions in mapping quantum circuits onto multi-core quantum computing architectures, focusing on minimizing non-local communications. It introduces the Hungarian Qubit Assignment (HQA) algorithm, which optimizes qubit assignments to cores to reduce inter-core communications. The paper derives theoretical bounds on the number of non-local communications for random quantum circuits and evaluates HQA against state-of-the-art mapping algorithms. The results show that HQA improves execution time and reduces non-local communications by 4.9× and 1.6×, respectively, compared to the best-performing algorithm. The paper highlights the potential of HQA as a scalable approach for mapping quantum circuits into multi-core architectures, positioning it as a valuable tool for advancing quantum computing at scale.