How can we avoid the dimensionality curse? Many possibilities

1. smarter basis functions
2. resummation of specific correlations
3. stochastic sampling of high-lying states (stochastic FCI, CC and SRG/IMSRG)
4. many more

Machine Learning and Quantum Computing hold also great promise in tackling the ever increasing dimensionalities. A hot new field is Quantum Machine Learning, see for example the recent textbook by Maria Schuld and Francesco Petruccione. Here we will focus on Machine Learning.