**Brunello Tirozzi (University of Rome)**

**Title:** Quantum neural networks, an immersion of classical neural networks in the domain of quantum computing

**Abstract:**
Neural networks arise as an intersection of different disciplines,
neurobiology, computer technology and statistical mechanics.
The retrieval and storage of information have been studied by the
specialists of these fields for many decades and many interesting
point of view and approaches have been exchanged with success for getting
interesting results. In particular neurobiological descriptions have been
incorporated in the well known Hopfield model which has been solved
exactly
with the cavity method. The difference with classical statistical
mechanics is that the Hopfield model is a mean field theory of classical
spins interacting through random interactions, the randomness being given
by the stored patterns.
In the first part of the talk I will describe
the methods and aims of this classical approach. In the second part I will
explain how to transfer this machinery in the field of quantum computing,
give the main definitions and illustrate how to estimate the states of
minimum energy of the quantum neural network.