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However, the efficiency of distributed optimization is often hindered by communication bottlenecks. To mitigate this, we propose the Quantized Riemannian Gradient Tracking (Q-RGT) algorithm, where agents update their local variables using quantized gradients. The introduction of quantization noise allows our algorithm to bypass the constraints of the accurate Riemannian projection operator (such as retraction), further improving iterative efficiency. To the best of our knowledge, this is the first algorithm to achieve an $\\mathcal{O}(1/K)$ convergence rate in the presence of quantization, matching the convergence rate of methods without quantization. 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To the best of our knowledge, this is the first algorithm to achieve an $\\mathcal{O}(1/K)$ convergence rate in the presence of quantization, matching the convergence rate of methods without quantization. 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