The possibility of 4x more dynamic range (2 stops) is very exciting. DPReview's writeup [1] mentions the possibility that each of the subpixels could be set to different sensitivities and that each one's information could contribute to the larger pixel's output, increasing its overall dynamic range at the expense of resolution. This simple approach isn't practical with the Bayer pattern because all adjacent pixels have different color filters.
EDIT: I actually found a little explainer on quad bayer on Sony's site [2] for an industrial sensor from 2017. Instead of changing each subpixel's sensitivity, they change how long the subpixel collects light.
[1] https://www.dpreview.com/news/0249781150/sony-imx586-smartph...
[2] https://www.sony-semicon.co.jp/products_en/new_pro/may_2017/...