Talks

Quantum generators are crucial objects for understanding quantum systems. They encode all the information required to predict the evolution of closed (Hamiltonians) and open memoryless dynamics (Lindbladians). Additionally, they offer structural insight into the noise affecting experimental implementations of quantum processes. In this talk, we will discuss the definition of continuous-time random unitary evolutions characterized by stochastic Hamiltonians, showing mixing properties and efficient convergence to the uniform measure over the unitary group. We will then consider the problem of embedding a quantum map into a Markovian evolution, presenting a scheme to extrapolate the full description of the Lindbladian that is the best fit for the tomographic measurements of any (noisy) quantum channel. Finally, we will introduce a new bound on quantum operators generated by arbitrary time-dependent Hamiltonians by leveraging a correspondence with binary trees structures. References: [1] E. Onorati et al., ‘Mixing properties of stochastic quantum Hamiltonians’, https://arxiv.org/abs/1606.01914 [2] E. Onorati et al., ‘Fitting quantum noise models to tomographic data’, https://arxiv.org/abs/2103.17243

Machine learning has significantly improved the way scientists model and interpret large datasets across a broad range of the physical sciences; yet, its "black box" nature often limits our ability to trust and understand its results. Interpretable and explainable AI is ultimately required to realize the potential of machine-assisted scientific discovery. I will review efforts toward explainable AI focusing in particular in applications within the field of Astrophysics. I will present an explainable deep learning framework which combines model compression and information theory to achieve explainability. I will demonstrate its relevance to cosmological large-scale structures, such as dark matter halos and galaxies, as well as the cosmic microwave background, revealing new physical insights derived from these explainable AI models.

As we've seen at this workshop, exciting progress has recently been made in the study of neural networks by applying ideas and techniques from theoretical physics. In this talk, I will discuss a precise relation between quantum field theory and deep neural networks, the NN/QFT correspondence. In particular, I will go beyond the level of analogy by explicitly constructing the QFT corresponding to a class of networks encompassing both vanilla feedforward and recurrent architectures. The resulting theory closely resembles the well-studied O(N) vector model, in which the variance of the weight initializations plays the role of the 't Hooft coupling. In this framework, the Gaussian process approximation used in machine learning corresponds to a free field theory, and finite-width effects can be computed perturbatively in the ratio of depth to width, T/N. These provide corrections to the correlation length that controls the depth to which information can propagate through the network, and thereby sets the scale at which such networks are trainable by gradient descent. This analysis provides a non-perturbative description of networks at initialization, and opens several interesting avenues to the study of criticality in these models.

We will examine the idea of Bayesian updating as an inverse diffusion like process and its relation to the exact renormalisation group. In particular we will look at the role of Fisher Information, its metric and possible physical interpretations.