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Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

The large scale distribution of matter in the Universe contains the answers to many mysteries, such as the nature of dark matter, the reionization of the Universe, and the growth of galaxies. Cosmological simulations are the only way to understand these questions. I will talk about how modern current simulation models, work, discuss some new models and improvements in our latest simulation runs, especially our implementations of reionization and cosmology. I will then talk about some new work to dramatically expand the region of applicability of these simulations using machine learning. This can both to expand their dynamic range and combine different simulations to infer the physical parameters of the Universe.

Gravitational wave observations are beginning to reveal the nature of the dark side of our universe. The Advanced LIGO and Virgo detectors have observed dozens of binary black hole mergers during the recent third observing run and, with planned sensitivity improvements, expect to observe significantly more binary black hole mergers in future observing runs. The combination of the increased number of detections  and the sheer volume of data associated with each detection provides a significant data analysis challenge. In recent years, various machine learning approaches such as convolutional neural networks have been explored as a basis for rapid analyses for gravitational wave data. This seminar will give a brief introduction to current transient gravitational wave data analysis methodology and highlight novel applications of machine learning for rapid detection of binary black holes and rapid inference of their astrophysical properties. The use of generative machine learning algorithms for transient gravitational wave signal generation will also be discussed.

With the race for quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum circuit. While such "supervised quantum models" are sometimes called "quantum neural networks", their mathematical structure reveals that they are in fact kernel methods with kernels that measure the distance between data embedded into quantum states. This talk gives an informal overview of the link, and discusses the far-reaching consequences for quantum machine learning.

I describe recent progress on a program of research aimed at finding a simultaneous completion of quantum mechanics and general relativity, while also addressing the question of how the universe chose its effective laws out of a vast landscape of possible laws.    This is based on a few principles:   time in the sense of causation is fundamental, as are events, and the views  of events (their backward celestial spheres.) Further the view of every event must be distinct from that of every other.  This is enforced by a choice for potential energy that maximizes the diversity of views of events, called the variety.    Given these postulates, everything else emerges dynamically, including space, spacetime, and quantum dynamics; as the variety turns out to reduce appropriately to Bohm’s quantum potential, which in turn is responsible for quantum non-locality, entanglement etc.  

A consequence of these ideas is that the effective low energy laws, including the values of the dimensionless constants of the standard model,  should evolve dynamically.    I present three realizations of this idea: cosmological natural selection (1992), the principle of precedence (2005), and the hypothesis that the universe may learn how to choose its vacuum out of a landscape of possible vacua through a process formally analogous to machine learning (2021).   I discuss the prospects for observational tests of these ideas.

At the technical level,  some of these ideas are related through the use of matrix modes whose actions are cubic in the matrices, which are tied to topological and gravitational theories.  At a methodological level, issues involving an interplay of reductionist and functionalist reasoning may be discussed.  

Collaborators on recent work include Stephon Alexander, Marina Cortes, William Cunningham,  Stuart Kauffman, Jaron Lanier,  Andrew Liddle,  Joao Magueijo,   Stefan Stanojevic,  Michael W. Toomey, Clelia Verde and Dave Wecker.

Agency accounts of causation are often criticised as being unacceptably subjective: if there were no human agents there would be no causal relations, or, at the very least, if humans had been different then so too would causal relations. Here we describe a model of a causal agent that is not human, allowing us to explore the latter claim.   

Our causal agent is special kind of open, dissipative physical system, maintained far from equilibrium by a low entropy source of energy, with accurate sensors and actuators. It has a memory to record sensor measurements and actuator operations, and a learning system that can access the sensor and actuator records to learn and represent the causal relations. We claim that causal relations are relations between the internal sensor and actuator records and the causal concept inherent in these correlations is then inscribed in the physical dynamics of the internal learning machine. We use this model to examine the relationships between three familiar asymmetries aligned with causal asymmetry: time's arrow, the thermodynamic arrow and the arrow of deliberation and action. We consider both classical and quantum agent models and illustrate some differences between the two. 
 

In the last two decades the field of nonequilibrium quantum many-body physics
has seen a rapid development driven, in particular, by the remarkable progress
in quantum simulators, which today provide access to dynamics in quantum
matter with an unprecedented control. However, the efficient numerical
simulation of nonequilibrium real-time evolution in isolated quantum matter
still remains a key challenge for current computational methods especially
beyond one spatial dimension. In this talk I will present a versatile and
efficient machine learning inspired approach. I will first introduce the
general idea of encoding quantum many-body wave functions into artificial
neural networks. I will then identify and resolve key challenges for the
simulation of real-time evolution, which previously imposed significant
limitations on the accurate description of large systems and long-time
dynamics. As a concrete example, I will consider the dynamics of the
paradigmatic two-dimensional transverse field Ising model, where we observe
collapse and revival oscillations of ferromagnetic order and demonstrate that
the reached time scales are comparable to or exceed the capabilities of state-
of-the-art tensor network methods.

With much of the cosmological information in the primary CMB having already been mined, the next decade of CMB observations will revolve around the secondary CMB lensing effect, which will touch nearly all aspects of observation in some way. At the same time, the increasingly low noise levels of these future observations will render existing "quadratic estimator" methods for analyzing CMB lensing obsolete. This leaves us in an exciting place where new methods need to be developed to fully take advantage of the upcoming generation of CMB data just on our doorstep. I will describe my work developing such new lensing analysis tool, made possible by Bayesian methods, modern statistical techniques, and borrowing ideas from machine learning. I will present the recent first-ever application of such methods to data (from the South Pole Telescope; https://arxiv.org/abs/2012.01709) and discuss prospects for this analysis in the future with regards to not just lensing but also primordial B modes, reionization, and extragalactic foreground fields.

Studying the smallest self-bound dark matter structure in our Universe can yield important clues about the fundamental particle nature of dark matter, and galaxy-scale strong gravitational lensing provides a unique way to detect and characterize dark matter on small scales at cosmological distances from the Milky Way. Research in this field can be broadly separated into works that aim to directly detect individual perturbers and works that aim to statistically constrain the matter distribution by looking at collective perturbations caused by an unresolved population of perturbers. We present recent advances in both of these approaches. With respect to the former, we present advances in the analysis of gravitational lenses and identification of small-scale clumps using machine learning. With respect to the latter, we introduce the convergence power spectrum as a promising statistical observable that can be extracted from strong lens images and used to distinguish between different dark matter scenarios, showing how different properties of the dark matter get imprinted on different scales. We include a discussion on the different contribution of substructure and line-of-sight structure to perturbations in strong lens images.

Majorana zero modes have attracted much interest in recent years because of their promising properties for topological quantum computation. A key question in this regard is how fast two Majoranas can be exchanged giving rise to a unitary gate operation. In this presentation I will first explain that the transport of Majoranas in one-dimensional topological superconductors can be formulated as a “simple” optimal control optimization problem for which we propose several different control regimes. Next I will discuss the optimization methods, Differential Programming and Natural Evolution Strategies, that were applied to the Majorana control problem and came up with a counter-intuitive transport strategy. This strategy, which we dubbed jump-move-jump, will form the focus of the last part of the presentation in which I explain the key underlying mechanisms behind the strategy by reformulating the motion of Majoranas in a moving frame. I will conclude by arguing that these results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems with performance levels that make it relevant to the realization of large-scale quantum technology.

We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied question in machine learning and statistics. In this work, we give the first sample-efficient algorithm for the quantum Hamiltonian learning problem. In particular, we prove that polynomially many samples in the number of particles (qudits) are necessary and sufficient for learning the parameters of a spatially local Hamiltonian in l_2-norm.
Our main contribution is in establishing the strong convexity of the log-partition function of quantum many-body systems, which along with the maximum entropy estimation yields our sample-efficient algorithm. Classically, the strong convexity for partition functions follows from the Markov property of Gibbs distributions. This is, however, known to be violated in its exact form in the quantum case. We introduce several new ideas to obtain an unconditional result that avoids relying on the Markov property of quantum systems, at the cost of a slightly weaker bound. In particular, we prove a lower bound on the variance of quasi-local operators with respect to the Gibbs state, which might be of independent interest.

Joint work with Srinivasan Arunachalam, Tomotaka Kuwahara, Mehdi Soleimanifar

Recently, a lot of attention has been dedicated to a novel class of topological systems, called higher-order topological insulators (TIs). The reason is that, while a conventional d-dimensional TI exhibits (d-1)-dimensional gapless boundary modes, a d-dimensional nth-order TI hosts gapless modes at its (d-n)-dimensional boundaries only, generalizing in this way the notion of bulk-boundary correspondence. In this talk I will show the results of our recent study of such systems in two and three dimensions. I will briefly describe a few specific proposals to engineer such systems in practice. I will also present a simple method which can be used to read out the resulting topological phase diagrams experimentally. I will conclude by saying why the higher-order TIs are promising to study the interplay of topology and interactions and how Machine learning can help us to better understand these novel topological states.