This study aims to enhance wireless communication efficiency by maximizing the sum rate through optimized rate allocation and power control for edge users in small cell networks. Small cells improve coverage and bandwidth in congested networks but face challenges such as interference and limited resources, particularly for users at the cell edge. This article introduces a Meta-LVQA technique to boost system throughput by optimizing rate allocation and power control, ensuring equitable resource distribution among users, and managing in-cell interference using Rate Splitting Multiple Access (RSMA). The problem is initially framed using classical methods. However, this manuscript employs the Meta-Learning Variational Quantum Algorithm (Meta-LVQA) to optimize the sum rate. Therefore, it is necessary to transform the classical equation into an equivalent quantum equation using a quantum circuit. Numerical results demonstrate that RSMA with Meta-LVQA consistently outperforms all other methods. Specifically, RSMA with Meta-LVQA surpasses RSMA with Variational Quantum Algorithm (VQA), NOMA with Meta-LVQA, and NOMA with VQA by and respectively, when the sum rate is measured against a minimum rate requirement of 1.15 Mbps at SCEU1. When computing the sum rate using four SCEUs, RSMA with Meta-LVQA outperforms RSMA with VQA, NOMA with Meta-LVQA, and NOMA with VQA by and respectively.