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The dynamics of closed quantum systems undergoing unitary processes has been well studied, leading to notions of measures for the expressive power of parameterized quantum circuits, relative to the unique, maximally expressive, average behaviour of ensembles of unitaries. Such unitary expressivity measures have further been linked to concentration phenomena known as barren plateaus. However, existing quantum hardware are not isolated from their noisy environment, and such non-unitary dynamics must therefore be described by more general trace-preserving operations. To account for hardware noise, we propose several, non-unique measures of expressivity for quantum channels and study their properties, highlighting how average non-unitary channels differ from average unitary channels. In the limit of large composite system and environments, average noisy quantum channels are shown to be maximally globally depolarizing. Furthermore, we rigorously prove that highly-expressive parameterized quantum channels will suffer from barren plateaus, thus generalizing explanations of noise-induced phenomena. We complement our analytical findings with numerical experiments that showcase that, in certain situations, noise can increase the expressivity of parametrized quantum circuits.

In this talk I show how simple ideas motivated from the Swampland program, lead to concrete predictions for our universe.  These include predictions for particle physics and cosmology.  I also discuss some experimental predictions for these ideas.

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Large neural networks are often studied analytically through scaling limits: regimes in which some structural network parameters (e.g. depth, width, number of training datapoints, and so on) tend to infinity. Such limits are challenging to identify and study in part because the limits as these structural parameters diverge typically do not commute. I will present some recent and ongoing work with Alexander Zlokapa (MIT), in which we provide the first solvable models of learning – in this case by Bayesian inference – with neural networks where the depth, width, and number of datapoints can all be large.

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The interplay of quantum fluctuations and interactions can yield novel quantum phases of matter with fascinating properties. Understanding the physics of such systems is a very challenging problem as it requires to solve quantum many body problems—which are generically exponentially hard to solve on classical computers. In this context, universal quantum computers are potentially an ideal setting for simulating the emergent quantum many-body physics. In this talk, I will discuss two different classes of quantum phases: First, we consider symmetry protected topological (SPT) phases and show that a topological phase transitions can be simulated using shallow circuits. We then utilize quantum convolutional neural networks (QCNNs) as classifiers and introduce an efficient framework to train them. Second, we focus on the realization of topological ordered phases and simulate the braiding of anyons. Taking into account additional symmetries, we then investigate phase transitions between different symmetry enriched topological (SET) phases.

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