### Understanding the LEarning process of QUantum Neural networks (LeQun)

Project Type: Prin 2022

Funded by: MUR

Period: Sep 28, 2023 – Sep 27, 2025

Budget: €8.858,00

Principal Investigator: Giacomo De Palma (Università di Bologna)

Local coordinator: Dario Trevisan (Università di Pisa)

##### Description

Quantum computers promise to be a revolutionary solution to fulfill the increasing need for high-performance computing, and quantum computing has been identified as a key intervention area in the “Programma Nazionale per la Ricerca 2021-27”. Determining the problems on which quantum computers can provide major advantages with respect to classical computers is the main theoretical problem of quantum computing and constitutes the challenge that LeQun addresses.
The most promising family of quantum algorithms that can be implemented on the forthcoming generation of quantum computers are variational quantum algorithms, also called quantum neural networks. Despite the promises, there is no problem of practical interest yet where quantum neural networks have a provable advantage over the best classical algorithms. A thorough theoretical study of the trainability, expressibility and generalization properties of quantum neural networks and of their potential advantages with respect to classical computers constitutes the main theoretical challenge of quantum machine learning.
LeQun will tackle this extremely ambitious challenge through the following objectives:
O1:
- To analytically characterize the probability distribution of the functions generated by trained quantum neural networks and determine their trainability and generalization performances.
- To study the training stability against imperfect outcomes of quantum measurements and the query complexity of the entire training process, namely the number of measurements that must be performed to achieve the desired accuracy.
O2:
- To identify the architectures of quantum neural networks that have the potential to provide major advantages with respect to classical computers and to perform a proof-of-principle validation of the advantages of the identified architectures using realquantum devices and simulators.
LeQun will tackle the challenge with an interdisciplinary approach that connects quantum machine learning with probability theory and quantum many-body physics. The strategy of LeQun is based on the recent breakthrough results in classical machine learning stating that in the mean-field limit of infinite width of the hidden layers, trained deep neural networks are equivalent to Gaussian processes. These results explained the unreasonably good performances of deep neural networks, and LeQun will generalize them to the quantum setting.
LeQun will constitute a successful example of interdisciplinary research and will foster a cross-fertilization among quantum computing, probability theory and many-body quantum physics. The results of LeQun will be highly relevant for all the researchers working on quantum computing and machine learning both in industry and academia, thus contributing to creating value for the whole society, and its results will constitute a fundamental contribution to the main challenge of quantum computing.