: Exact results on dynamics of dual unitary circuits and their perturbations
Tomaz Prosen (University of Lubiana)
I will review the recent results on the proof of random matrix spectral form factor and explicit computation of correlation functions of local observables in the so-called dual-unitary brickwork circuits (including integrable, non-ergodic, ergodic and chaotic cases). Further I will show how these results can be extended to another quantum-circuit platform, specifically to unitary interactions round-a-face (IRF). I will argue that correlation functions of these models are generally perturbatively stable with respect to breaking dual-unitarity, and describe a simple result within this framework.
Exceptional Spectral Phase in a Dissipative Collective Spin Model
Alaro Rubio (IFF-CSIC)
We study a model of a quantum collective spin weakly coupled to a spin-polarized Markovian environment and find that the spectrum is divided into two regions that we name normal and exceptional Liouvillian spectral phases. In the thermodynamic limit, the exceptional spectral phase displays the unique property of being made up exclusively of second order exceptional points. As a consequence, the evolution of any initial density matrix populating this region is slowed down and cannot be described by a linear combination of exponential decays. This phase is separated from the normal one by a critical line in which the density of Liouvillian eigenvaluesdiverges, a phenomenon analogous to that of excited-state quantum phase transitions observed in some closed quantum systems. In the limit of no bath polarization, this criticality is transferred onto the steady state, implying a dissipative quantum phase transition and the formation of a boundary time crystal.
Seminar Room, Serrano 113b
Probing the entanglement structure of quantum states via partial-transpose moments.
Benoit Vermesch (CNRS Grenoble)
I will discuss our works on partial-transpose moments, which are quantities that can be measured experimentally in quantum technologies using randomized measurements.In particular, I will present the p3-PPT condition introduced in  that has been experimentally used to detect mixed-state entanglement in a trapped-ion quantum system. I will then show  that these PT moments can also be used to reveal the entanglement structure of many-body quantum states. PT moments provide in particular order parameters for the three mixed-state entanglement phases of Haar random states, and show striking differences for various classically simulatable states.  Phys. Rev. Lett. 125, 200501 (2020) Votto, Carrasco, Kokail, Kraus, Zoller, Vermersch, to appear on arxiv
Characterizing the loss landscape of variational quantum circuits
Alexandre Dauphin (ICFO)
Machine learning techniques enhanced by noisy intermediate-scale quantum (NISQ) devices and especially variational quantum circuits (VQC) have recently attracted much interest and have already been benchmarked for certain problems. Inspired by classical deep learning, VQCs are trained by gradient descent methods which allow for efficient training over big parameter spaces. For NISQ sized circuits, such methods show good convergence. There are however still many open questions related to the convergence of the loss function and to the trainability of these circuits in situations of vanishing gradients. Furthermore, it is not clear how ‘good’ the minima are in terms of generalization and stability against perturbations of the data and there is, therefore, a need for tools to quantitatively study the convergence of the VQCs. In this talk, I will discuss how one can compute the Hessian of the loss function of VQCs and how to characterize the loss landscape with it. I will also discuss how this information can be interpreted and compared to classical neural networks. I will then show some benchmark of our results on several examples, starting with a simple analytic toy model to provide some intuition about the behaviour of the Hessian, then going to bigger circuits, and also train VQCs on data.
Fundamental physics at the quantum limits of measurement
Dan Carney (Berkley)
Over the past decade, a number of searches for fundamental physics signals have reached the point where their sensitivity is limited not by technical noise but by quantum mechanics itself. These include searches for gravitational waves, a number of dark matter candidates, and even quantum signatures of gravity. I will give a brief overview of some of these ideas and experiments, and highlight some of the main open questions and directions for the next decade
On universality out of equilibrium
Luca Tagliacozzo (IFF-CSIC)
I will review the reasons beyond our recent quest of universality out of equilibrium using as a motivation several example of scaling theory developed at equilibrium.