  The quadratic rough Heston model provides a natural way to encode Zumbach
effect in the rough volatility paradigm. We apply multi-factor approximation
and use deep learning methods to build an efficient calibration procedure for
this model. We show that the model is able to reproduce very well both SPX and
VIX implied volatilities. We typically obtain VIX option prices within the
bid-ask spread and an excellent fit of the SPX at-the-money skew. Moreover, we
also explain how to use the trained neural networks for hedging with
instantaneous computation of hedging quantities.
