## Stationary states of non-Hermitian lattice models: why the non-Hermitian skin effect does not tell the whole story

Alexander Mc Donald (Universidad de Chicago)

15:00 14-06-2022

Non-Hermitian lattice models have received an enormous amount of attention in recent years, in part because they violate seemingly-obvious intuition found in any Hermitian model. The paradigmatic example is the non-Hermitian skin effect (NHSE), in which a non-Hermitian Hamiltonian exhibits a striking sensitivity to boundary conditions; the spectrum and eigenvectors under open boundary conditions in no way resembles its periodic system counterpart. While the dynamics of such models have received some attention, the same can not be said for the stationary states of such models. This is especially relevant in a quantum setting, where dissipation used to realize non-Hermiticity must be accompanied by unavoidable fluctuations.In this talk, I will discuss how a generic non-Hermitian tight-binding model can be realized in a quantum-mechanically consistent manner by constructing an appropriate open quantum system. Focusing on a quantum realization of the Hatano-Nelson model, I will demonstrate how the non-Hermitian skin effect alone cannot be used to predict relevant steady-state properties. I will instead argue that propagation physics, as encoded by the systems Green’s function, is the relevant object that controls the steady state. Using this quantity, we are able to understand both why the steady state occupation is controlled by a macroscopic length scale and why this real-space density is markedly different for bosons versus fermions. How work highlights the importance of characterizing a non-Hermitian Hamiltonian beyond its eigenvalues and eigenvectors.

Seminar Room, Serrano 113b

## Quantum-inspired solutions for privacy leaks in machine learning

Alejandro Pozas (UCM)

12:00 07-06-2022

Physics research has not been alien to the recent success of machine learning techniques. Unlike other disciplines, physics is in a unique position to influence research in machine learning as well. In this talk, I will argue and practically illustrate that insights in quantum information, concretely coming from the tensor network representations of quantum many-body states, can help in devising better privacy-preserving machine learning algorithms. After a short introduction to privacy in machine learning, I will show that standard neural networks are vulnerable to a type of privacy leak that, a priori, is resistant to standard protection mechanisms. Afterwards, I will show that tensor networks, when used as machine learning architectures, are invulnerable to this leak. The proof of resilience is based on the existence of canonical forms for such architectures. Given the growing expertise in training tensor networks and that these architectures are recently showing to compete and even surpass traditional machine learning architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed when using machine learning on sensitive data. This talk is based on arXiv:2202.12319.

Online seminar

## Unconventional quantum optics in non-Hermitian baths

Miguel Bello (MPQ-Munich)

12:00 31-05-2022

In this talk I will give an overview of the peculiar effects that occur when quantum emitters interact with one-dimensional non-Hermitian environments. First, we will discuss the presence of “hidden” bound states, which are the non-Hermitian analogue of the vacancy-like bound states present in Hermitian systems. This will be exemplified with the Hatano-Nelson model. Then, we will see how in critical baths, in the sense that their spectrum has a vanishing damping gap, it is possible to observe algebraic emitter decay, which typically is hindered in Hermitian systems by the presence of stable bound states. I will try to relate this strongly non-Markovian behavior with the dynamics within the bath.Refs:[1] https://arxiv.org/abs/2205.05479[2] https://arxiv.org/abs/2205.05490

Online seminar

## Optical response of two-dimensional arrays of nanostructures

Alejandro Manjavacas (Instituto de Optica)

12:00 24-05-2022

Periodic arrays are an exceptionally interesting arrangement for plasmonic nanostructures due to their ability to support strong collective lattice resonances, which arise from the coherent multiple scattering enabled by the array periodicity. Thanks to these exceptional properties, periodic arrays are being exploited in a wide variety of applications, including ultrasensitive biosensing, nanoscale light emission, and color printing, to cite a few. In this seminar, we will discuss some recent theoretical advances on the topic of lattice resonances and show how these collective modes can mediate an efficient long-range coupling between dipole emitters placed near the array that supports them.

Seminar Room, Serrano 121 (CFMAC)

## : Exact results on dynamics of dual unitary circuits and their perturbations

Tomaz Prosen (University of Lubiana)

12:00 03-05-2022

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.

Online seminar

## Exceptional Spectral Phase in a Dissipative Collective Spin Model

Alaro Rubio (IFF-CSIC)

14:00 27-04-2022

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)

12:00 05-04-2022

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 [1] that has been experimentally used to detect mixed-state entanglement in a trapped-ion quantum system. I will then show [2] 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. [1] Phys. Rev. Lett. 125, 200501 (2020)[2] Votto, Carrasco, Kokail, Kraus, Zoller, Vermersch, to appear on arxiv

Online seminar

## Characterizing the loss landscape of variational quantum circuits

Alexandre Dauphin (ICFO)

12:00 29-03-2022

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.

Online seminar

## Fundamental physics at the quantum limits of measurement

Dan Carney (Berkley)

16:00 08-03-2022

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

Online seminar

## On universality out of equilibrium

Luca Tagliacozzo (IFF-CSIC)

12:00 18-01-2022

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.

Online seminar