Talks

In this talk I address the problem of simultaneously inferring unknown quantum states and unknown quantum measurements from empirical data. This task goes beyond state tomography because we are not assuming anything about the measurement devices. I am going to talk about the time and sample complexity of the inference of states and measurements, and I am going to talk about the robustness of the minimal Hilbert space dimension. Moreover, I will describe a simple heuristic algorithm (alternating optimization) to fit states and measurements to empirical data. For this algorithm the dataset does not need to be quantum. Hence, the proposed algorithm enables us to interpret general datasets from a quantum perspective. By analyzing movie ratings, we demonstrate the power of quantum models in the context of item recommendation which is a key discipline in machine learning. We observe that quantum models can compete with state-of-the-art algorithms for item recommendation. Based on joint work with Aram Harrow. Relevant preprints: arXiv:1412.7437 and arXiv:1510.02800.

The condensation of bosons can induce transitions between topological quantum field theories (TQFTs). This as been previously investigated through the formalism of Frobenius algebras and with the use of Vertex lifting coefficients. I will discuss an alternative, algebraic approach to boson condensation in TQFTs that is physically motivated and computationally efficient. With a minimal set of assumptions, such as commutativity of the condensation with the fusion of anyons, we can prove a number of theorems linking boson condensation in TQFTs with algebra extensions in conformal field theories and with the problem of factorization of completely positive matrices over the positive integers. I will present an algorithm for obtaining a condensed theory fusion algebra and its modular matrices. In addition, I will discuss how this formalism can be used to build multi-layer TQFTs which could be a starting point to build three-dimensional topologically ordered phases. Using this formalism, I will also give examples of bosons that cannot undergo a condensation transition due to topological obstructions.

We consider quantum quench from a gapped to a gapless system in 1+1 dimensions. We 

provide a rigorous proof of the thermalization of the reduced density matrix, hence that of

an arbitrary string of local operators in an interval. In case the system is integrable, the "thermalization" leads to a generalized Gibbs ensemble (GGE). We model the critical quench in terms of an initial state in terms of a conformal boundary state deformed by exponential cutoffs involving hamiltonian and other charges. We justify this choice of the initial state by explicitly

deriving it in free boson and free fermion systems with time-dependent mass. A surprising result we find is that for generic quenches and observables the higher charges remain 

important even if the initial gap is arbitrarily high, contrary to standard RG expectations.

( based on hep-th/1501.04580  and a couple of upcoming papers)

Despite being ubiquitous throughout the Universe, the fundamental physics governing dark matter remains a mystery. While this physics plays little role in the current evolution of large-scale cosmic structures, it did have a major impact in the early epochs of the Universe on the evolution of cosmological density fluctuations on small causal length scales. Studying the astrophysical structures that resulted from the gravitational collapse of fluctuations on these small scales can thus yield important clues about the physics of dark matter. Today, most of these structures are locked in deep inside the potential wells of galaxies, making the study of their properties difficult. Fortunately, due to fortuitous alignments between high-redshift bright sources and us, some of these galaxies act as spectacular strong gravitational lenses, allowing us to probe their inner structure. In this talk, we present a unified framework to extract information about the power spectrum of gravitational potential fluctuations inside any type of lens galaxies. We argue that fully exploiting this new approach will likely require a paradigm shift in how we describe structures on sub-galactic scales. We finally discuss which properties of mass substructures are most readily constrained by lensing data.

In this talk, I will revise some of the aspects that lead isolated interacting quantum systems to thermalize.

In the presence of disorder, however, the thermalization process fails resulting in a phenomena where 

transport is suppressed known as many-body localization. Unlike the standard Anderson localization for 

non-interacting systems, the delocalized (ergodic) phase is very robust against disorder even for moderate

values of interaction. Another interesting aspect of the many-body localization phase is that under the time

evolution of the quenched disorder, information present in the initial state may survive for arbitrarily long times.

This was recently used as a probe of many-body localization of ultracold fermions in optical lattices

with quasi-periodic disorder [1]. Here, we will stress that this analysis may suffer from substantial finite-size effects 

after comparing with the numerical results in one-dimensional Hubbard chains [2].

References:

[1] - M.Schreiber, S. S. Hodgman,. P. Bordia,.H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, I. Bloch, Science 349, 842 (2015)

[2] - Rubem Mondaini and Marcos Rigol, Phys. Rev. A 92, 041601(R) (2015)