Talks

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://github.com/dwohns/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

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

https://github.com/dwohns/PI-Summer-School-2020