Colloquium

Quantum mechanics is a cornerstone of modern physics. Just as the 19th century was called the Machine Age and the 20th century the Information Age, the 21st century promises to go down in history as the Quantum Age. Quantum Computing promises unprecedented speed in solving certain classes of problems while Quantum Cryptography promises unconditional security in communications. In this talk, I will discuss the world of single and entangled photons and also discuss ongoing work towards quantum computing, quantum information and quantum cryptography in our Quantum Information and Computing lab at the Raman Research Institute, Bengaluru. I will end with our broad vision for the future, which includes establishment of long distance secure quantum communications in India and beyond involving satellite based, fibre based as well as integrated photonics based approaches towards the global quantum internet.

Zoom Link: https://pitp.zoom.us/j/94788493307?pwd=QTlUaTY4Nm1IS3hyeUFIbVFKV3RMQT09

Mirror symmetry and time-invariance violating processes were crucial at establishing the Standard Model of fundamental interactions as we know it, their tiny effects eventually measured after enormous experimental effort. Macroscopic material on the other hand can maximally break these symmetries spontaneously. Inside these materials, Dark Matter can exhibit phenomena otherwise impossible in the vacuum. In this talk, I will discuss such a phenomenon that we call the piezoaxionic effect: In crystals whose structure breaks mirror symmetry, which are broadly known as piezoelectric, dark matter candidates called axions will produce a change in the crystals size, i.e. strain. Such a strain can be detected with well-established methods leading to a new observable for this well-motivated class of Dark Matter candidates.

Zoom Link: https://pitp.zoom.us/j/96153495346?pwd=QU1MTENUTzdNOU5sZVc3VzY4NHI1UT09

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

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

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

Quantum error correction and symmetries are two key notions in quantum information and physics. The competition between them has fundamental implications in fault-tolerant quantum computing, many-body physics and quantum gravity. We systematically study the competition between quantum error correction and continuous symmetries associated with a quantum code in a quantitative manner. We derive various forms of trade-off relations between the quantum error correction inaccuracy and three types of symmetry violation measures. We introduce two frameworks for understanding and establishing the trade-offs based on the notions of charge fluctuation and gate implementation error. From the perspective of fault-tolerant quantum computing, we demonstrate fundamental limitations on transversal logical gates. We also analyze the behaviors of two near-optimal codes: a parametrized extension of the thermodynamic code, and quantum Reed–Muller codes.

Zoom Link: TBD

The first direct detection of gravitational waves from merging black holes in 2015 has opened up new avenues to studying gravity in the strong-field regime, inferring the mass and spin distributions of astrophysical black holes and probing the nature of ultra-dense nuclear matter in the interior of neutron stars. Seven years on, we count approximately 100 detections of gravitational waves from compact binary mergers.
 
These observations are goldmines for precise measurements of the source properties and the discovery of new physics at the edge of our current understanding. Pioneering innovations in detector technology will soon let us put black holes under a microscope, allowing us to push Einstein's theory of gravity to the limit. To do so will require exquisitely accurate theoretical models for the emitted gravitational-wave signal if we are to unlock the full discovery potential.

In this talk, I will discuss some of the most spectacular discoveries from the third observing run of Advanced LIGO and Virgo and their implications. I will also highlight some of the pitfalls and challenges in interpreting gravitational-wave detections.

Zoom Link: https://pitp.zoom.us/j/96161151229?pwd=NExyMitMaWpMTVBsL0VRTjZNbFBvZz09

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.

What is the global symmetry of Nature? In the absence of gravity, the most obvious answer to this question is given by special relativity and is associated with the Poincare transformations. As was noted a long time ago, the free Maxwell equations have a wider symmetry group - the 15 parameters conformal invariance, containing in addition to ten Poincare generators, four special conformal transformations, and dilatations. Dilatations change the length of the rulers, while special conformal transformation can bend the lines but do not alter the angles between them. Could it be that the symmetry of all interactions is conformal? We will show that the answer to this question is "yes". The essential feature of the theory is the anomaly-free extension of the spontaneously broken conformal symmetry to curved space-time. We discuss how the effective Lagrangian respecting this special Weyl symmetry can be used for the description of particle phenomenology and cosmology.

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.