In this tutorial, I will cover recent advances in developing learning theory for quantum machines. The tutorial will focus on the basic techniques for establishing prediction guarantees in quantum machine learning models and the fundamental ideas for proving the advantages of quantum machines over classical machines in learning from experiments.

OPENING

Speaker: Michele Grossi & Alberto Di Meglio

The core computational tasks in quantum systems are the computation of expectations of operators, including reduced density matrices, and the computation of the ground state energy of a quantum system. Many tools have been developed in the literature to achieve this, including Density Functional Theory (DFT), Density Matrix Renormalization Group (DMRG) and other Tensor Network methods,...

Abstract: There is no shortage of quantum machine learning papers observing that a particular quantum model "beats its classical counterparts on real-world datasets". However, the subtlety of choices made in benchmark experiments, the small scale of the models and data, as well as narratives influenced by the commercialisation of quantum technologies carry the danger of a strong positivity...

Abstract: Variational quantum computing schemes have received considerable attention due to their high versatility and potential to make practical use of near-term quantum devices. Despite their promise, the trainability of these algorithms can be hindered by barren plateaus (BPs) induced by the expressiveness of the parametrized quantum circuit, the entanglement of the input data, the...

Abstract:

Although still a relatively niche field in classical machine learning, topological data analysis has raised substantial interest from the perspective of quantum algorithms in the last few years.

In this talk we will introduce the topic of topological data analysis, and discuss the state-of-art of quantum algorithms for this problem, together with their promises and limitations,...

What can we quantum-learn in the age of noisy quantum computation? Both more and less than you think. Noise limits our ability to error-mitigate, a term that refers to near-term schemes where errors that arise in a quantum computation are dealt with in classical pre-processing. I present a unifying framework for error mitigation and an analysis that strongly limits the degree to which quantum...

Quantum error correction will ultimately empower quantum computers to

leverage their full potential. However, substantial device overhead and

the need for frequent syndrome measurements, which are themselves

error-prone, render the demonstration of logical qubits that

significantly surpass break-even still challenging. Autonomous quantum

error correction represents a promising...