Classical simulation of quantum circuits with neural-network states

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 discuss advances in the classical variational representations of many-qubit states based on artificial neural networks.

First I will present results concerning the expressive power of neural-network quantum states, 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 discuss machine-learning-based techniques useful to simulate large structured quantum circuits, beyond what is currently accessible with other classical approaches.