About that useful little corner of Hilbert space and its neural network representations

The vast majority of quantum states of interest for practical applications have distinctive features and intrinsic structure. These typically occupy only a very limited corner of the vast manifold of allowed quantum states, making them often amenable for compact classical representations.

In this talk I will overview a recently introduced classical representation of many-qubit states based on artificial neural networks.

First I will present results concerning their expressive power, rewiewing representation theorems and arguing that these representations are not limited by the amount of entanglement they can encode.In this context, I will also show a new explicit and polynomially efficient mapping from contractible tensor-network states.

Then, I will show several applications of these variational representations, with a focus on quantum computing applications. Most notably, I will focus on a variational technique useful to simulate large structured quantum circuits, as well as applications of classical neural-network states to benchmark and improve NISQ quantum hardware.