Colloquium

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.

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.

The understanding of strongly-correlated quantum matter has challenged physicists for decades. The discovery three years ago of correlated phases and superconductivity in magic angle twisted bilayer graphene led to the emergence of a new materials platform to investigate strongly correlated physics, namely moiré quantum matter. These systems exhibit a plethora of quantum phases, such as correlated insulators, superconductivity, magnetism, Chern insulators, and more. In this talk I will review some of the recent advances in the field, focusing on the newest generation of moiré quantum systems, where correlated physics, superconductivity, and other fascinating phases can be studied with unprecedented tunability. I will end the talk with an outlook of some exciting directions in this emerging field.

There has been much theorizing on the question of how the procedures of quantum theory might modify general relativity, perhaps leading to a resolution of the problem of the space-time singularities of gravitational collapse. However, I shall argue that these procedures cannot, alone, resolve the space-time singularity issue. Instead, I shall maintain that considerations of relativity, both special and general, could well provide pointers to how the major conundrum of quantum mechanics—the collapse of the wave-function—may eventually be resolved, via curious retro-active aspects of quantum and classical reality.

An important and unresolved question in cosmology today is whether there is new physics that is missing from our current standard Lambda Cold Dark Matter (LCDM) model. A current discrepancy in the measurement of the Hubble constant could be signaling a new physical property of the universe or, more mundanely, unrecognized measurement uncertainties. I will discuss two of our most precise methods for measuring distances in the local universe: Cepheids and the Tip of the Red Giant Branch (TRGB). I will present new results from the Carnegie-Chicago Hubble Program (CCHP), the goal of which is to independently measure a value of the Hubble constant to a precision and accuracy of 2%. Using the Hubble Space Telescope Advanced Camera for Surveys,  we are  using the TRGB to calibrate Type Ia supernovae. I will  address the uncertainties,  discuss the current tension in Ho, and whether there is need for additional physics beyond the standard LCDM model.

The problem of quantum gravity -- i.e. to determine the microscopic structure underlying quantum mechanical theories that reproduce general relativity at long distances -- is a major outstanding problem in modern physics.  Solving the quantum gravitational scattering problem is one sharp way to address this question.  While in principle effective field theory (EFT) provides a systematic framework for solving scattering problems, in quantum gravity the complete answer requires an infinite number of measurements and thereby fails to predict details of the microscopic structure.

I will present two developments that provide new insight into the gravitational scattering problem.   The first is a class of infinite-dimensional symmetries generically found to arise in gauge and gravitational scattering.  The infinite number of constraints implied by the symmetries are equivalent to quantum field theoretic soft theorems, which prescribe the pattern of soft radiation produced during a scattering event.  The second development is a reformulation of the gravitational scattering problem in which Lorentz symmetry is rendered manifest and realized as the action of the global conformal group in two dimensions.  This reformulation, which involves scattering particles of definite boost weight as opposed to energy, offers a new approach precisely because it does not admit the decoupling of low and high-energy physics that underpins the traditional EFT approach.  I will describe new perspectives ensuing from these developments on various properties of the gravitational scattering problem, including collinear limits, infrared divergences and universal behavior associated to black hole formation. 

Have you always wanted to know: What the symmetries of nature are? How black holes process quantum information? What the ultimate UV description of our universe is? Then join me as I continue to develop a new framework to describe scattering:  Celestial Holography.

The Celestial Holography framework applies the holographic principle to spacetimes with vanishing cosmological constant by mapping 4D S-matrix elements to correlators in a 2D conformal field theory. This map possesses a number of surprising features. For example, it emphasizes infinite dimensional symmetry enhancements, which are typically hidden in IR factorization theorems for amplitudes; reorganizes collinear limits as CFT operator product expansions; and mixes UV and IR behavior in a manner that may allow us to make general claims about scattering not obvious from perturbation theory.

Can we show that the UV behavior of amplitudes must be stringy? Can we bootstrap celestial CFTs? Can we unify tools from Loop Quantum Gravity and String Theory?

Maybe, with your help!

No. Obviously not. It's a daft question. But, buried underneath
this daft question is an extremely interesting one: is it possible to
simulate the known laws of physics on a computer? Remarkably, there is a
mathematical theorem, due to Nielsen and Ninomiya, that says the answer is
no. I'll explain this theorem, the underlying reasons for it, and some
recent work attempting to circumvent it.

In this talk, I will review the recent advances in the understanding of intriguing infinite-dimensional symmetries that emerge at the boundary of asymptotically flat spacetime and in the vicinity of black hole horizons. These symmetries play an important role in the description of many phenomena such as gravitational memory effects and scattering amplitudes, and have paved the way to a holographic description of gravity in asymptotically flat spacetimes in terms of correlators on the celestial sphere.