You also misunderstand what is happening. Google did not do that. Google further trained the original model with an objective of minimizing error when quantized to 4-bit. The BF16 QAT is not an upscaled 4-bit model. When quantized to 4-bit, it should lose less accuracy than a typical 16-bit model loses when quantized to 4-bit, but the loss is not zero, because it is not based on a 4-bit model.

The Gemma 3 QAT report was a bit clearer:

https://developers.googleblog.com/en/gemma-3-quantized-aware...

"Instead of just quantizing the model after it's fully trained, QAT incorporates the quantization process during training. QAT simulates low-precision operations during training to allow quantization with less degradation afterwards for smaller, faster models while maintaining accuracy. Diving deeper, we applied QAT on ~5,000 steps using probabilities from the non-quantized checkpoint as targets. We reduce the perplexity drop by 54% (using llama.cpp perplexity evaluation) when quantizing down to Q4_0."

The BF16 is just trained to be more resistant to simulated quantization, which helps when it is actually quantized. Google is not doing post-training on the 4-bit model directly.