Physics

In his May 5 Perimeter Public Lecture webcast, Harvard professor L. Mahadevan will take viewers on a journey into the mathematical, physical, and biological workings of morphogenesis to demonstrate how scientists are beginning to unlock many of the secrets that have vexed scientists since Darwin.

Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. I'll explain two approaches to understanding the behavior and the operational significance of quantum complexity in many-body systems. First, I'll consider a simple model on n qubits: We create a random quantum circuit by randomly sampling the gates that compose it. In this model, quantum complexity can be shown to grow linearly in the number of gates until saturating at a value that is exponential in n. This result proves a version of a conjecture by Brown and Susskind in the context of quantum gravity, thereby reinforcing our understanding of the evolution of wormholes in holography. Second, I'll discuss how quantum complexity manifests itself in the operational processes that we can carry out on an n-qubit system. For instance, what resources are necessary to reset an n-qubit memory register to the pure all-zero computational basis state? This approach reveals a connection between thermodynamics and complexity, as we exhibit a trade-off between the thermodynamic work cost that is necessary for the reset procedure and the complexity cost of the procedure. The general trade-off is quantified by a new measure of entropy which directly connects complexity with entropy. I'll discuss the implications of our results and new prospects for many-body physics in the regime where quantum states are of ever increasing complexity.

Joint work with: Jonas Haferkamp, Teja Naga Bhavia Kothakonda, Anthony Munson, Jens Eisert, Nicole Yunger Halpern

The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk, I outline a brief history of the theorems, explain a bit of the language, translate the first theorem into coordinate invariant language and give a few examples. I will mention briefly their historical importance in physics and integrable systems. In the second part of the talk, I describe why they are still relevant: why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of surfaces of Bill Thurston and the open problems in higher dimensions. I will finish by mentioning two recent papers, one in math and the other in physics, which greatly simplify the derivations of important identities by using the theorems.

Zoom Link: https://pitp.zoom.us/j/96748003059?pwd=aElYTlNXVlY4dEhtcmd0YUcvOHZIdz09

LIGO and Virgo have observed over 80 gravitational-wave sources to date, including mergers between black holes, neutron stars, and mixed neutron star- black holes. The origin of these merging neutron stars and black holes -- the most extreme objects in our Universe -- remains a mystery, with implications for stars, galaxies and cosmology. I will review the latest LIGO-Virgo discoveries and discuss some recent astrophysical lessons, including mass gaps, black hole evolution with cosmic time, and implications for cosmology. While the latest gravitational-wave observations have answered a number of longstanding questions, they have also unlocked new puzzles. I will conclude by discussing what we can expect to learn from future gravitational-wave and multi-messenger discoveries.

Zoom Link: https://pitp.zoom.us/j/94857758725?pwd=MW1PNXZRNkFGL25xUkpjVWlabmNJZz09

The black hole information paradox — whether information escapes an evaporating black hole or not —  remains one of the greatest unsolved mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in the deep quantum gravity regime. Recent developments in the holographic dictionary and in particular its application to entanglement, however, have shown that a semiclassical analysis of gravitational physics has a hallmark feature of unitary evolution. I will describe this recent progress and discuss some potential new avenues for working towards a resolution of the information paradox.

The patent system is designed to help innovators protect their intellectual property. In this colloquium, we will discuss logistical and strategic aspects of the patent process, to help you better understand how to leverage the patent system. Topics will include the anatomy of a patent, deadlines and procedural steps for filing patent applications, and strategic considerations in developing the claims and other components of a patent application.

Zoom Link: https://pitp.zoom.us/j/91402107798?pwd=UDRQV0IvY3JEUkVJeC9QR3JXVjZSdz09

Thermodynamics has shed light on engines, efficiency, and time’s arrow since the Industrial Revolution. But the steam engines that powered the Industrial Revolution were large and classical. Much of today’s technology and experiments are small-scale, quantum, far from equilibrium, and processing information. Nineteenth-century thermodynamics needs re-envisioning for the 21st century. Guidance has come from the mathematical toolkit of quantum information theory. Applying quantum information theory to thermodynamics sheds light on fundamental questions (e.g., how does entanglement spread during quantum thermalization? How can we distinguish quantum heat from quantum work?) and practicalities (e.g., quantum engines and the thermodynamic value of coherences). I will overview how quantum information theory is being used to revolutionize thermodynamics in quantum steampunk, named for the steampunk genre of literature, art, and cinema that juxtaposes futuristic technologies with 19th-century settings.

Zoom Link: https://pitp.zoom.us/j/92454766615?pwd=QzZXMnYwN3ZZOTE5RzZEcHp6TkhMdz09

We develop a general approach to "interpret" what a network has learned by introducing strong inductive biases. In particular, we focus on Graph Neural Networks. 

The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

In particular, we will show examples of recovery of newton's law and masses of solar system bodies with real ephemeris data and recovery of navier-stokes equations with turbulence dataset.  We will speculate what one can do with this new tool.
 

Recent advances in quantum simulation experiments have paved the way for a new perspective on strongly correlated quantum many-body systems. Digital as well as analog quantum simulation platforms are capable of preparing desired quantum states, and various experiments are starting to explore non-equilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and time scales. State-of-the art quantum simulators provide single-site resolved quantum projective measurements of the state. Depending on the platform, measurements in different local bases are possible. The question emerges which observables are best suited to study such quantum many-body systems.

In this talk, I will cover two different approaches to make the most use of these possibilities. In the first part, I will discuss the use of machine learning techniques to study the thermalization behavior of an interacting quantum system. A neural network is trained to distinguish non-equilibrium from thermal equilibrium data, and the network performance serves as a probe for the thermalization behavior of the system. We apply this method to numerically simulated data, as well experimental snapshots of ultracold atoms taken with a quantum gas microscope. 

In the second part of this talk, I will present a scheme to perform adaptive quantum state tomography using active learning. Based on an initial, small set of measurements, the active learning algorithm iteratively proposes the basis configurations which will yield the maximum information gain. We apply this scheme to GHZ states of a few qubits as well as ground states of one-dimensional lattice gauge theories and show an improvement in accuracy over random basis configurations.