Colloquium

We will discuss quantum singular value transformation (QSVT), a simple unifying framework for quantum linear algebra algorithms developed by Gilyén, Low, Su, and Wiebe. QSVT is often applied to try to achieve quantum speedups for machine learning problems. We will see the typical structure of such an application, the barriers to achieving super-polynomial quantum speedup, and the state of the literature that's attempting to bypass these barriers. Along the way, we'll also see an interesting connection between quantum linear algebra and classical sampling and sketching algorithms(explored in the form of "quantum-inspired" classical algorithms).

We will begin by explaining the black hole information paradox, starting from first principles. We will then explain how computations in string theory yield a resolution of this paradox. When we make a bound state of strings and branes, then this bound state is found to swell up into a horizon sized `fuzzball'; this fuzzball radiates like a normal body without any information loss. The existence of these fuzzballs implies a new picture for the quantum gravitational vacuum, where the virtual fluctuations resemble the scale free fluctuations at a second order phase transition, rather than being confined to within the planck scale.  We will see how this `vecro' picture of the vacuum might give a resolution to several puzzles we face in cosmology, like the origin of energy needed for inflation and the existence of a cosmological constant.

The double copy relates scattering amplitudes in gauge theory and gravity. But interaction potentials (and spacetime metrics) can be extracted from amplitudes, and so the double copy leads to a relationship between classical solutions of gauge theory and gravity. In this talk I will describe this relationship, provide a perspective on the Schwarzschild metric as a “square” of the Coulomb charge, and take a look at the “square root” of the Kerr metric.

In the last few years there have been demonstrations of quantum advantage using noisy quantum circuits that are believed to go beyond the limits of the classical computers that exist today.  In this talk I will give an overview of a different type of quantum advantage that can be attained by shallow (short-depth) quantum circuits.  I will discuss recent results which establish unconditionally that constant-depth quantum circuits can solve certain linear algebra problems faster than their classical counterparts. We will see that the reason quantum computers solve these problems provably faster (as measured by circuit depth) than classical computers is due to a strong form of quantum nonlocality that is present in their input/output statistics. 

Zoom Link: https://pitp.zoom.us/j/96752851897?pwd=R29GWHovN0MwVXVYWklaNE1QZ1c5dz09

In 1930, the famous statistician and geneticist Ronald Fisher claimed to have proved a "fundamental theorem of natural selection". He compared this result to the second law of thermodynamics, and described it as holding "the supreme position among the biological sciences". But others found it obscure, and in its most obvious interpretation it is simply false. Luckily there is a true result closely resembling Fisher's claim: a general theorem connecting dynamical systems and information theory. I'll explain this, give the very simple proof, and draw a few conclusions.

Zoom Link: https://pitp.zoom.us/j/99898585189?pwd=NytLaWt2RjFPOTVJOEptMlBBd1BvZz09

The power of quantum information lies in its capacity to be non-local, encoded in correlations among entangled particles.  Yet our ability to produce, understand, and exploit such correlations is hampered by the fact that the interactions between particles are ordinarily local.  I will report on experiments in which we use light to engineer non-local interactions among cold atoms, with photons acting as messengers conveying information between them.  We program the spin-spin couplings in an array of atomic ensembles by tailoring the frequency spectrum of an optical control field.  We harness this programmability to access interaction graphs conducive to frustration and to explore quantum spin dynamics in exotic geometries and topologies.  More broadly, advances in optical control of interactions open new opportunities in areas ranging from quantum technologies to fundamental physics.  I will touch on implications for quantum-enhanced sensing, combinatorial optimization, and simulating quantum gravity.

I will present a single idea about representation which allows several recent advances in neural networks  to be combined into an imaginary system called GLOM.  GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. The talk will discuss the many ramifications of this idea.  If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by neural nets when applied to vision or language.  

The remarkable properties of electrons moving through crystalline lattices continue to surprise us. Recently, electrons in artificial moiré lattices have emerged as an extraordinary new platform. The simplest such moiré material consists of a pair of graphene sheets twisted relative to one another. At a  "magic" angle of about 1 degree, a variety of phenomena, including strong-coupling superconductivity, is observed. In this talk, I will review this rapidly moving field and describe our theoretical ideas that invoke the geometry of quantum states and topological textures like skyrmions. Finally, I will explain how these insights indicate a promising new family of moiré materials, twisted trilayer graphene, which is currently under active experimental study.

Quantum computers need to manipulate quantum states, and the only ways we know of doing this are inherently noisy. Thus, if we are ever to be able to do long computations on quantum computers, we need to make them fault tolerant. The way we know how to do this currently is to use quantum error correcting codes. We will introduce error correcting codes and explain how they can be used to provide fault tolerance for quantum computers.
 

We will discuss the recent advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Specifically, we will describe our recent technical upgrades that now allow the control over 200 atoms in two-dimensional arrays. Recent results involving the realization  of exotic phases of matter, study of quantum phase transitions and  exploration of  their non-equilibrium dynamics will be presented. In particular, we will report on realization and probing of quantum spin liquid states - the exotic states of matter have thus far evaded direct experimental detection. Finally,  realization and testing  of quantum optimization algorithms using such systems will be discussed.

Statistical mechanics is the branch of physics that explains how macroscopic properties of matter emerge from the behavior of its microscopic constituents. Population ecology studies how and why populations change over time and space, primarily due to the interaction among individuals and between individuals and the environment where they thrive. Although seemingly very different, both disciplines aim to explain large-scale phenomena based on a description of their underlying drivers, and statistical mechanics tools have been largely used to formalize population ecology. For over 100 years, however, mathematical models in population ecology have relied on very strong and unrealistic assumptions about the way individuals move and get to interact with each other and with the environment. Specifically, they assume that individuals behave like the molecules of an ideal gas: following completely random trajectories through the entire area occupied by the population and only interacting with each other when their trajectories intersect. 

In this presentation, I will first discuss why mathematical models are powerful tools to understand ecological processes. Then, I will show how traditional models of population dynamics emerge from ideal gas assumptions for individual movement and briefly touch on our recent efforts to refine those models combining more elaborated tools from statistical physics, random walk theory, and GPS tracking data of natural populations.

In this lecture we will show that the E8 and Leech lattices minimize energy of every potential function that is a completely monotonic function of squared distance (for example, inverse power laws or Gaussians). This theorem implies recently proven optimality of E8 and Leech lattices as sphere packings and broadly generalizes it to long-range interactions. The key ingredient of the proof is sharp linear programming bounds. To construct the optimal auxiliary functions attaining these bounds, we prove a new interpolation theorem. This is the joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko.