Large language models (LLMs) are revolutionizing how we interact with technology, but their massive size presents a challenge for deployment. Quantization, a technique that reduces the precision of the model's numerical representation (think of it like rounding off numbers), offers a powerful solution for shrinking LLMs and making them run faster. However, aggressive quantization, particularly to 2-bit precision, often leads to a significant drop in accuracy. Existing methods for compensating for this loss of accuracy haven't been entirely successful, especially with 2-bit quantization. This is where RILQ (Rank-Insensitive LoRA-based Quantization Error Compensation) comes in. RILQ tackles the problem of accuracy degradation in 2-bit quantized LLMs by cleverly leveraging LoRA (Low-Rank Adaptation), a popular technique for efficiently fine-tuning LLMs. Previous attempts to use LoRA for quantization error compensation faltered because they assumed the errors were low-rank, which isn't true for 2-bit quantization. RILQ addresses this by taking a more holistic approach. Instead of focusing on individual parts of the model, RILQ looks at the entire model's output and adjusts the LoRA adapters across all layers cooperatively. This allows it to effectively compensate for the high-rank errors introduced by 2-bit quantization. Tests on popular LLMs like LLaMA-2 and LLaMA-3 show that RILQ consistently improves accuracy with various state-of-the-art quantizers. It's particularly effective with LLaMA-3, which is known to be more sensitive to quantization. Moreover, RILQ is efficient—it requires minimal extra computational resources, making it a promising approach for deploying smaller, faster, and more accurate LLMs in real-world applications. This research opens doors to more accessible and efficient AI, paving the way for broader adoption across various devices and platforms.