Talks

Given a vector in a representation, can it be distinguished from zero by an invariant polynomial? This classical question in invariant theory relates to a diverse set of problems in mathematics and computer science. In quantum information, it captures the quantum marginal problem and recent bounds on tensor ranks. We will see that the general question can be usefully thought of as an optimization problem and discuss how this perspective leads to efficient algorithms for solving it.

We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS3 regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it. The low-energy limit of these correlations is precisely that of a double-scaled random matrix ensemble with Virasoro symmetry. Our findings suggest that if pure three-dimensional gravity has a holographic dual, then the dual is an ensemble which generalizes random matrix theory.

In this talk, I will discuss emergent criticality in non-unitary random quantum dynamics. More specifically, I will focus on a class of free fermion random circuit models in one spatial dimension. I will show that after sufficient time evolution, the steady states have logarithmic violations of the entanglement area law and power law

correlation functions. Moreover, starting with a short-range entangled many-body state, the dynamical evolution of entanglement and correlations quantitatively agrees with the predictions of two-dimensional conformal field theory with a space-like time direction. I will argue that this behavior is generic in non-unitary free quantum dynamics with time-dependent randomness, and show that the emergent conformal dynamics of two-point functions arises out of a simple" nonlinear master equation".

COVID-19 is a mysterious disease associated with a large number of unanswered questions. 

In this talk we review what is currently known, what is still a mystery and highlight some of our recent work on the role of climate, blood type and vaccinations on the transmission of the disease and on the extent of "dark infections", the asymptomatic and untested proportion of infections. We end with a list of open research questions that may be amenable to techniques from physics and data science.

The inference of the present expansion rate from the Cosmic Microwave Background and other early-time probes (assuming standard
cosmology) is in significant tension with several direct measurements of the same quantity. If this discrepancy is not due to unresolved systematics, it could provide strong evidence for physics beyond the standard models of particle physics and cosmology. I will describe a few simple models that attempt to alleviate this Hubble tension. All of these scenarios contain additional energy density of new light particles at early times with interactions that modify the background cosmology and evolution of density perturbations in the early universe. First, I will motivate the existence of a decaying component of dark matter with a significant free-streaming length as a means of addressing this tension. Then I will consider models with self-interacting neutrino or dark radiation components. I will show that such scenarios face stringent cosmological and laboratory constraints. As a result, in these examples, the tension can be alleviated but not eliminated altogether.

Recently, a lot of attention has been dedicated to a novel class of topological systems, called higher-order topological insulators (TIs). The reason is that, while a conventional d-dimensional TI exhibits (d-1)-dimensional gapless boundary modes, a d-dimensional nth-order TI hosts gapless modes at its (d-n)-dimensional boundaries only, generalizing in this way the notion of bulk-boundary correspondence. In this talk I will show the results of our recent study of such systems in two and three dimensions. I will briefly describe a few specific proposals to engineer such systems in practice. I will also present a simple method which can be used to read out the resulting topological phase diagrams experimentally. I will conclude by saying why the higher-order TIs are promising to study the interplay of topology and interactions and how Machine learning can help us to better understand these novel topological states.

Exact diagonalization part 3: Expectation values and correlation functions in the  Ising model GS, using these and energy gaps to identify a quantum phase transition; Demonstration of using matrix product states for the Ising model

https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020

We propose a reinforcement learning (RL) scheme for feedback quantum control within the quantum approximate optimization algorithm (QAOA). QAOA requires a variational minimization for states constructed by applying a sequence of unitary operators, depending on parameters living in a highly dimensional space. We reformulate such a minimum search as a learning task, where a RL agent chooses the control parameters for the unitaries, given partial information on the system. We show that our RL scheme learns a policy converging to the optimal adiabatic solution for QAOA found by Mbeng et al. arXiv:1906.08948 for the translationally invariant quantum Ising chain. In presence of disorder, we show that our RL scheme allows the training part to be performed on small samples, and transferred successfully on larger systems. Finally, we discuss QAOA on the p-spsin model and how its robustness is enhanced by reinforce learning. Despite the possibility of finding the ground state with polynomial resources even in the presence of a first order phase transition, local optimizations in the p-spsin model suffer from the presence of many minima in the energy landscape. RL helps to find regular solutions that can be generalized to larger systems and make the optimization less sensitive to noise.

References

https://arxiv.org/abs/2003.07419

https://arxiv.org/abs/2004.12323

Topology and path integrals

https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020

Representation theory, symmetries in quantum mechanics

https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020

Exact diagonalization part 2: Continue with finding matrices for N-site Ising model,  solve for eigenvalues and eigenstates of model

https://drive.google.com/drive/folders/1L6a1YCdB9EejAUmZ52oLDAeB6oosjwhU?usp=sharing

https://www.dropbox.com/sh/sprq2u40e3leoso/AADhyov350QS9TEDdgtErekCa?dl=0

https://github.com/gsellaroli/pi-summer-school-2020