Scientific Series

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. In the first part, I will show that standard neural networks are vulnerable to a type of privacy leak that involves global properties of the data used for training, thus being a priori resistant to standard protection mechanisms. In the second, I will show that tensor networks, when used as machine learning architectures, are invulnerable to this vulnerability. The proof of the resilience is based on the existence of canonical forms for such architectures. Given the growing expertise in training tensor networks and the recent interest in tensor-based reformulations of popular 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.

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We explore the physical consequences of embedding Einstein gravity with negative cosmological constant in Conformal Gravity in four dimensions. In the bulk, the procedure is equivalent to Holographic Renormalization, as the Einstein-AdS action appears augmented by the correct boundary counterterms. In codimension-2, 4D Conformal Gravity induces a 2D conformal invariant, which leads to a renormalized area for minimal surfaces attached to the conformal boundary. For arbitrary surfaces, this proposal reproduces other energy functionals as Willmore Energy and Reduced Hawking Mass. In particular, this procedure provides a more geometric approach to the computation of Holographic Entanglement Entropy for CFTs dual to 4D Einstein gravity.

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Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using associative information: maximize expected utility. There is an ongoing debate around the origin of probabilities involved in such calculation. In this work, we will show how the probabilities for decision-making can be grounded in causal models by considering decision problems in which the available actions and consequences are causally connected. In this setting, actions are regarded as an intervention over a causal model. Then, we extend a previous causal decision-making result, which relies on a known causal model, to the case in which the causal mechanism that controls some environment is unknown to a rational decision-maker. In this way, action-outcome probabilities can be grounded in causal models in known and unknown cases. Finally, as an application, we extend the well-known concept of Nash Equilibrium to the case in which the players of a strategic game consider causal information.

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Finite density systems can be described by effective field theories with non-linearly realized space-time symmetries, whose construction resembles that of the QCD chiral lagrangian. Based on that similarity, one would expect the construction to work equally well classically and quantum mechanically. While that is true for superfluids and solids, one instead finds that for genuine fluids things are made more complicated by the unusual dynamics of their transverse modes, which are not described by a Fock space. Focussing on the incompressible limit for a fluid in 2+1 dimensions, I illustrate its analogy with the ordinary rigid body. Indeed both systems describe motion on a group manifold. Proceeding from this analogy I develop  a consistent quantum mechanical description of a perfect fluid using the known equivalence between the area preserving diffeomorfism group in 2D and SU(N) for N->\infty

Light bosons, including light axions, dark photons, and dilaton/moduli, are well motivated extensions to the Standard Model of particle physics and intriguing dark matter candidates. Much progress has been made in recent years in both astrophysical and lab searches for these light bosons with the understanding that these light bosons act like weak classical waves which permeate the space we occupy. 

In this talk, I will discuss some novel phenomenon of light bosons in the dark sector, based on important in medium effects of these particles. I will show how to take advantage of medium effects of the photon to optimize searches for these light bosons with data coming from cosmic microwave background (CMB) experiments, and improve sensitivity to light dark photons and axions by orders of magnitude. I will also show how thinking of dark photon as weak classical waves breaks down during production of light bosons in both early and late universe, when gauged strings are produced in an event we call the string Bosenova, as well as the resulting observable consequences.

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Minimizing the energy of a many-body system is a fundamental problem in many fields. Although we hope a quantum computer can help us solve this problem better than classical computers, we have a very limited understanding of where a quantum advantage may be found. In this talk, I will present some recent theoretical advances that shed light on quantum advantages in this domain. First, I describe rigorous analyses of the Quantum Approximate Optimization Algorithm applied to minimizing energies of classical spin glasses. For certain families of spin glasses, we find the QAOA has a quantum advantage over the best known classical algorithms. Second, we study the problem of finding a local minimum of the energy of quantum systems. While local minima are much easier to find than ground states, we show that finding a local minimum under thermal perturbations is computationally hard for classical computers, but easy for quantum computers.

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Holographic conformal field theories exhibit dramatic changes in the structure of their operator algebras in the limit where the number of local degrees of freedom (N) becomes infinite. An important example of such phenomena is the violation of the additivity property for algebras associated to local subregions. We investigate the consequences of this "additivity anomaly" in the context of holographic duality. We propose that the difference in volumes of bulk dual subregions can be used as a holographic measure for this additivity anomaly of large N boundary algebras. We demonstrate how the additivity anomaly underlies the success of quantum error correcting code models of holography. Finally, we argue that the connected wedge theorems (CWTs) of May, Penington, Sorce, and Yoshida can be re-phrased in terms of the additivity anomaly, allowing for the definition of a generalized scattering region for which a generalization of the CWTs can be formulated such that both the theorem and its converse should hold.

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Weak measurements can be viewed as a soft projection that interpolates between an identity operator and a projection operator, and can induce an effective central charge distinct from the unmeasured CFT. In the first part, I will discuss the effect of measurement and postselection on the critical ground state of a Luttinger liquid theory. Depending on the Luttinger parameter K, the effect of measurement is irrelevant, marginal, or relevant, respectively. When the measurement is marginal, and we find a critical state whose entanglement entropy exhibits a logarithmic behavior with a continuous effective central charge as a function of measurement strength. Inspired by this result, in the second part, I will discuss a holographic description of the weak measurement. The weak measurement is modeled by an interface brane, separating different geometries dual to the post-measurement state and the unmeasured CFT. In an infinite system, the weak measurement is related to ICFT via a spacetime rotation. We find that the holographic entanglement entropy with twist operators located on the defect is consistent in both calculations for ICFT and weak measurements. In a finite system, the weak measurement can lead to a rich phase diagram, in which the post-measurement geometry can realize a Python’s lunch.

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Causal discovery aims at learning causal relations among variables from data. It is an emerging field at the interface of machine learning and statistics that found ample application in several disciplines. From a physicist's point of view it can be seen as an operational definition of the concept of causal relation between variables, especially in an observational context where experimental manipulation is precluded. Interestingly, causal discovery has not yet been applied to Astronomy, despite it being the observational science par excellence. Here I will present the first application of causal discovery to Astronomy with the goal of addressing a debated issue in galaxy formation: the origin of the observed scaling relations between supermassive black hole (SMBH) and host galaxy properties. I apply three causal discovery algorithms to a state-of-the-art dataset of SMBH host galaxies with dynamical mass measurements, with the goal of learning a causal structure in terms of a directed acyclic graph. The results are consistent between methods and are amenable to physical interpretation, showing that across the multiplicity of possible causal structures, in elliptical galaxies SMBH mass is predominantly an effect of galaxy properties while in spiral galaxies the reverse holds. I offer an explanation of this finding in terms of the physics of galaxy merging, and address the limitations and the theoretical implications of this new method for galaxy formation in some detail.

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Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. Here we explore the surprising connection between symmetry-protected topology (SPT) and separability of their boundary mixed states. More specifically, we consider lattice systems in d space dimensions with anomalous symmetry G, where the anomaly is characterized by a bulk SPT invariant in the group cohomology Hd+2(G,U(1)). We show that any mixed state ρ that is strongly symmetric under G, in the sense that G ρ ∝ ρ, is necessarily (d+2)-nonseparable, i.e. is not the mixture of tensor products of d+2 states in the Hilbert space. Furthermore, such states cannot be prepared from any (d+2)-separable states using finite-depth local quantum channels, so the non-separability is long-ranged in nature. The anomaly-nonseparability connection also allows us to generate simple examples of mixed states with nontrivial multi-partite entanglement.

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In this talk I will discuss the rich interplay of light particles with density. In particular, I will show that the couplings of the QCD axion get modified in high density conditions. I will discuss the implications on astrophysical constraints, such as supernova and neutron star bounds. I will then look at the impact that axion-like particles can have on the structure of neutron stars