Nick Hunter-Jones: Sharp transitions in quantum circuit complexity

The circuit complexity of a unitary or quantum state is defined as the size of the shortest quantum computation that implements the unitary or prepares the state. The complexity of a time-evolved state is thought to grow linearly in time for generic many-body systems. This linear growth has now been proven for random quantum circuits, using their convergence to approximate unitary designs. In this talk we’ll discuss some interesting transitions that occur when considering the complexity of open quantum systems. We’ll end by mentioning a few complexity growth conjectures inspired by holographic theories.

Cécilia Lancien: Quantum expanders - Random constructions & Applications

The goal of the talk will be to understand what quantum expanders are, what they are useful for, and how they can be constructed. We will first recall the definition of classical expander graphs, and explain how quantum analogues of these objects can be defined. We will then show that, both classically and quantumly, random constructions typically provide examples of optimal expanders. In the quantum case, such result is derived from a spectral analysis for random matrix models with a tensor product structure. Finally, we will present implications in terms of typical decay of correlations in 1D many-body quantum systems with local interactions. 

The talk will be based mostly on the following works: https://arxiv.org/abs/1906.11682 (with David Perez-Garcia), https://arxiv.org/abs/2302.07772 (with Pierre Youssef) and https://arxiv.org/abs/2409.17971.

Marcin Lis: The Ising magnetization field and the Gaussian free field

I will define an (alternative to the FK-random cluster model) Edwards-Sokal representation of the Ising model using random currents. I will then discuss a scaling limit result which implies that the continuum Ising magnetization field and the Gaussian free field are naturally coupled. To the best of our knowledge, the existence of such a coupling was not predicted before. This completes the picture of bosonization of the planar Ising model. Based on joint work in progress with Tomas Alcalde and Lorca Heeney.

Mohammed Osman: Eigenvalue and Eigenvector Statistics of non-Hermitian Random Matrices

We will discuss recent results on local statistics of eigenvalues and eigenvectors of non-Hermitian random matrices, with a focus on the use of partial Schur decomposition to study matrices with a small Gaussian component.