Distributed quantum computing (DQC) offers a promising approach to scale quantum computing by overcoming the resource limitations of a single quantum processor. However, inter-node communication remains a major bottleneck of DQC due to inefficient and error-prone entanglement distribution. Optimizing inter-node communication can not only reduce the amount of entanglement resource needed to execute a quantum circuit but also improve execution speed and accuracy of the results. This paper proposes DPRQ, a qubit routing algorithm for minimizing inter-node communication in distributed quantum circuits divided into collective communication blocks. Unlike current approaches that utilize greedy block-level qubit routing strategies, DPRQ employs a dynamic programming-based technique focused on global circuit-level optimization, while capturing inter-block dependencies. We evaluated DPRQ on four sets of quantum circuits and a variety of DQC configurations. The results demonstrate that DPRQ's innovative routing strategy achieves an average of 24.40% reduction with a maximum of 85.06% reduction in inter-node communication, when compared to the state-of-the-art collective communication-based DQC compiler QuComm.

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