Talks

Abstract: Randomness is a powerful resource for information-processing applications. For example, classical randomness is essential for modern information security and underpins many cryptographic schemes. Similarly, quantum randomness can protect quantum information against noise or eavesdroppers who wish to access or manipulate that information. These observations raise a set of related questions: How quickly and efficiently can we generate quantum randomness? How much quantum randomness is necessary for a given task? What can we use quantum randomness for? In this talk, I address these questions using all-to-all Brownian circuits, a family of random quantum circuits for which exact results can often be obtained via mean-field theory. I will first demonstrate that all-to-all Brownian circuits form k-designs in a time that scales linearly with k. I will then discuss how these circuits can be applied to study Heisenberg-limited metrology and quantum advantage. In particular, I will discuss a time-reversal protocol that can achieve Heisenberg-limited precision in cavity QED and trapped ion setups; I will also discuss the application of these circuits to studying classical spoofing algorithms for the linear cross-entropy benchmark, a popular measure of quantum advantage.

The long-range force between neutrinos is poorly constrained. In the late-time universe, a long-range force that is a few orders of magnitude stronger than gravity can induce Jeans perturbation instability in the non-relativistic cosmic neutrino background, drastically changing its large-scale behavior. In this talk, I will describe how the cosmic neutrino background evolves and forms nonlinear bound states in the presence of a long-range force. I will then discuss the impact of these neutrino bound states on the matter structures in the universe, and the constraints due to the absence of these signals.

Deviations from a parity-symmetric Universe would strongly signal the presence of new physics beyond the Standard Model. The lowest-order scalar observable sensitive to parity in a homogeneous and isotropic Universe is the connected four-point function of a given cosmological field. Geometrically, this function is described by a suitable average of this field over many tetrahedral configurations. As the CMB represents a spherical projection of three-dimensional curvature fluctuations, its four-point function serves as a unique, but potentially limited, probe of this fundamental symmetry. In this talk, I will discuss progress in rigorously understanding the CMB’s sensitivity to parity-violating physics from both early- and late-time sources.

We will discuss some aspects of my recent preprint, joint with Victor Ginzburg, on Kostant-Whittaker reduction, a (deformation) quantization of restriction to a Kostant slice. We will explain how this functor can be used to prove conjectures of Ben-Zvi and Gunningham on parabolic induction, as well as a convolution exactness conjecture of Braverman and Kazhdan in the D-module setting. While this talk will occasionally reference facts from a talk I gave at Perimeter on other aspects of this preprint, the overlap and references will be minimal.

The physics of strongly correlated systems offers some of the most intriguing physics challenges such as competing orders or the emergence of dynamical composite degrees of freedom. Often, the resolution of these physics challenges is computationally hard, but can be simplified by a formulation in terms of the appropriate dynamical degrees of freedom.