Physics

This colloquium is presented in collaboration with the Foundations of Quantum Computational Advantage conference. 

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Abstract TBA

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Ground states as well as Gibbs states of many-body quantum Hamiltonians have been studied extensively since the inception of quantum mechanics. In contrast, the landscape of many-body quantum states that are not in thermal equilibrium is relatively less explored. In this talk I will discuss some of the recent progress in understanding decohered or dissipative quantum many-body states. One of the key ideas I will employ is that of "separability", i.e., whether a mixed state can be expressed as an ensemble of short-range entangled pure states. I will discuss several quantum phase transitions in topological phases of matter subjected to Markovian environmental noise from a separability viewpoint, and argue that such a framework also subsumes our understanding of pure quantum states as well as Gibbs states. Time permitting, I will also provide a brief overview of quantum spin-systems subjected to non-Markovian noise originating from an electronic bath, and discuss a new critical phase of matter where quantum coherence coexists with dissipation.

References: 2307.13889, 2309.11879, 2310.07286

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Characterizing metastable states and saddle points in complex systems can shed light on a variety of equilibrium and out-of-equilibrium behaviors. In this talk, I will discuss the most versatile theoretical technique for this, the Kac–Rice method, and its application to a family of mean-field models, the spherical spin glasses. I will draw connections from this technique to random matrix theory and Faddeev–Popov gauge fixing. For the spherical models, writing down an effective action is straightforward but finding physical saddle points can be challenging. I will show how, for the lowest-energy states, a BRST supersymmetry can be used to simplify the action and map it to a more tractable equilibrium problem. Finally, I will discuss challenges to using these techniques in inference problems with non-Gaussian energy functions, and current work being done to address them.

Eukaryotic cells and bacteria can use the substrate to self-regulate their movement. Eukaryotic cells, such as MDCK epithelial cells, leave footprints on the substrate, which are then used to regulate their motility and exploratory behavior. On the other hand, Escherichia coli bacteria stop and adhere to the surface to break confinement when swimming close to the surface and explore their surroundings more efficiently. In this talk, I will explore these mechanisms through mathematical models highlighting how both cells and bacteria, at two different biological scales, use the environment to self-regulate the way they explore their surroundings.

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.

From quenched physical systems to simple optimization algorithms, descent in an energy or cost landscape is thought to underpin many interesting phenomena. Likewise, the geometry of this landscape is thought to explain diverse outcomes of this descent: in those with few minima, the lowest are easily found; while in those with very many, getting stuck among a proliferation of high minima is overwhelmingly likely. In mean-field spin glasses and inference problems, we can hope to use geometry to explain when transitions between these behaviors occur and which kind of minima will typically be found. I will describe the past success of this approach in the simplest spin glass models and its recent failure in slightly less simple ones. I will share several new results on the statistics and arrangement of metastable states and saddle points which together indicate that traditional mean-field geometric tools may not be able to answer everything. Finally, I share some thoughts on what extensions might be needed to precisely predict where descent goes.

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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