ShamAN-Q is a sub-1-bit post-training quantization method for large language models (LLMs), building on the NanoQuant method. It uses a tractable dense curvature metric and Kullback-Leibler minimization to fit a Kronecker product to the empirical Fisher information matrix. ShamAN-Q improves perplexity on the WikiText-2 dataset and matches zero-shot accuracy on the Eleuther LM Evaluation Harness.