Random unitaries form the backbone of numerous components of quantum technologies, and serve as indispensable toy models for complex processes in quantum many-body physics. In all of these applications, a crucial consideration is in what circuit depth a random unitary can be generated. I will present recent work, in which we show that local quantum circuits can form random unitaries in exponentially lower circuit depths than previously thought. We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over n qubits in log n depth. In a similar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in poly log n depth, and in all-to-all-connected circuits in poly log log n depth. These shallow quantum circuits have low complexity and create only short-range entanglement, yet are indistinguishable from unitaries with exponential complexity. Applications of our results include proving that classical shadows with 1D log-depth Clifford circuits are as powerful as those with deep circuits, demonstrating superpolynomial quantum advantage in learning low-complexity physical systems, and establishing quantum hardness for recognizing phases of matter with topological order.

Galaxies are the medium through which we study the structure of the universe. However, widely applied statistical models of galaxies are generally over-simplified: even recently proposed models cannot capture the dependencies on environment or formation history. To solve this problem, I will introduce Graph Neural Networks (GNNs), a general and ideal tool for physical modelling. Geometrically constrained GNNs vastly improve our models, and allow us to ask detailed questions about the importance of formation history and environment for cosmological galaxy modeling. I will also prove a surprising equivalence between these two aspects of galaxy formation.

In this talk, I will discuss how M2-M5 intersections in a twisted M-theory background yield the R-matrices of the quantum toroidal algebra of gl(1). These R-matrices are identified with the Miura operators for the q-deformed W- and Y-algebras. Additionally, I will show how the M2-M5 intersection (or equivalently, the Miura operator) generates the qq-characters of the 5d N=1 gauge theory, offering new insight into the algebraic meaning of the latter.

To justify the existence of measurements that can not be performed jointly on quantum systems, Heisenberg put forward a heuristic argument, involving the famous gamma-ray microscope Gedankenexperiment, based on the existence of measurements that irreversibly alter the physical system on which they act. Today, the impossibility of jointly measuring some physical quantities, termed measurement incompatibility, and irreversible disturbance, namely the existence of operations that irreversibly alter the system on which they act, are understood to be distinct but related features of quantum mechanics. In our work, we formally characterized the relationship between these two properties, showing that measurement incompatibility implies irreversible disturbance, though the converse is false. The counterexamples are two toy theories: Minimal Classical Theory and Minimal Strongly Causal Bilocal Classical Theory. These two are distinct as counterexamples because the latter allows for classical conditioning. Our research followed an operational approach exploiting the framework of Operational Probabilistic Theories. In particular, it required the development of two new classes of operational theories: Minimal Operational Probabilistic Theories and Minimal Strongly Causal Operational Probabilistic Theories. These theories are characterized by a restricted set of dynamics, limited to the minimal set consistent with the set of states. In Minimal Strongly Causal Operational Probabilistic Theories, classical conditioning is also allowed.

I present an overview of the work I have done over the last few years on the phase space structure of gauge theories in the presence of boundaries. Starting with primers on the covariant phase space and symplectic reduction, I then explain how their generalization when boundaries are present fits into the reduction-by-stages framework. This leads me to introduce the concept of (classical) superselection sectors, whose physical meaning is clarified by a gluing theorem. Applying the framework developed this far to a null hypersurface, I then discuss how the extension of the Ashtekar-Streubel symplectic structure by soft modes emerges naturally, and how electric memory ties to superselection. If time allows, and depending on the audience’s interests, I will finally compare reduction-by-stages with the edge-mode formalism or discuss its relation to dressings and “gauge reference frames”. An overarching theme will be the nonlocal nature of gauge theories. This seminar is based on work done with Gomes and Schiavina.
References:
The general framework: 2207.00568
Null Yang-Mills: 2303.03531
Gluing: 1910.04222
A pedagogical introduction: 2104.10182
Dressings and reference frames: 1808.02074, 2010.15894, 1608.08226

Quasinormal modes of a black hole are closely related to the dynamics of the spacetime near the horizon. In this connection, the black hole ringdown phase is a powerful probe into the nature of gravity. However, the challenge of computing quasinormal mode frequencies has meant that ringdown tests of gravity have largely remained model-independent. In this talk, I will introduce Metric pErTuRbations wIth speCtral methodS (METRICS) [1], a novel spectral scheme capable of accurately computing the quasinormal mode frequencies of black holes, including those with modifications beyond Einstein's theory or the presence of matter. I will demonstrate METRICS' accuracy in calculating quasinormal mode frequencies within general relativity, as a validation, and its application to Einstein-scalar-Gauss-Bonnet gravity [2, 3], an example of modified gravity theory to which METRICS has been applied. I will also present preliminary results from applying METRICS to dynamical Chern-Simons gravity. Finally, I will discuss potential future applications of METRICS beyond computing black hole quasinormal modes.
[1]: https://arxiv.org/abs/2312.08435
[2]: https://arxiv.org/abs/2405.12280
[3]: https://arxiv.org/abs/2406.11986

In my talk I will explain how to extend the Goncharov-Kenyon class of cluster integrable systems by their Hamiltonian reductions. In particular, this extension allows to fill in the gap in cluster construction of the q-difference Painlev'e equations. Isomorphisms of reduced Goncharov-Kenyon integrable systems are given by mutations in another, dual in non-obvious sense, cluster structure. These dual mutations cause certain polynomial mutations of dimer partition functions and polygon mutations of the corresponding decorated Newton polygons.

A resource theory imposes a preorder over states, with one state being above another if the first can be converted to the second by a free operation, and where the set of free operations defines the notion of resourcefulness under study. In general, the location of a state in the preorder of one resource theory can constrain its location in the preorder of a different resource theory. It follows that there can be nontrivial dependence relations between different notions of resourcefulness.
In this talk, we lay out the conceptual and formal groundwork for the study of resource dependence relations. In particular, we note that the relations holding among a set of monotones that includes a complete set for each resource theory provides a full characterization of resource dependence relations. As an example, we consider three resource theories concerning the about-face asymmetry properties of a qubit along three mutually orthogonal axes on the Bloch ball, where about-face symmetry refers to a representation of $\mathbb{Z}_2$, consisting of the identity map and a $\pi$ rotation about the given axis. This example is sufficiently simple that we are able to derive a complete set of monotones for each resource theory and to determine all of the relations that hold among these monotones, thereby completely solving the problem of determining resource dependence relations. Nonetheless, we show that even in this simplest of examples, these relations are already quite nuanced.
At the end of the talk, we will briefly discuss how to witness nonclassicality in quantum resource dependence relations and demonstrate it with the about-face asymmetry example.
The talk is based on the preprint: arXiv:2407.00164 and ongoing work.

The Cherenkov Telescope Array Observatory (CTAO) is the upcoming next-generation ground-based very-high-energy (VHE) gamma-ray observatory. The CTAO will significantly advance the study of VHE gamma-rays through a combination of wider field of view, substantially increased detection area, and superior angular and spectral resolution over an energy range extending from tens of GeV to hundreds of TeV. Full-sky coverage will be achieved using two independent Imaging Air Cherenkov Telescope (IACT) arrays: one in the northern hemisphere (Canary Islands, Spain) and one in southern hemisphere (Paranal, Chile). The CTAO will explore a wide range of science topics in high-energy astrophysics, including the origin of higher-energy cosmic rays, mechanisms for particle acceleration in extreme environments, and astroparticle phenomena that may extend the Standard Model of particle physics. In this talk, I will outline the broad science potential of the CTAO and provide the CTAO’s current status and timeline. I will also describe the contributions of the CTAO-US collaboration to CTAO, including the development of an ultra-high resolution Schwarzschild-Couder telescope for VHE astronomy and the emergence of UV-band optical astronomy at the sub-100 micro-arcsecond angular scale.

The generation of large scales white noise is a generic property of the dynamics of physical systems described by local non-linear partial differential equations. Non-linearities prevent the small scale dynamics to be erased by smoothing. Unresolved small scale dynamics act as an uncorrelated (white or Poissonian) noise (seemingly stochastic but actually deterministic) contribution to large scale dynamics. Such is the case for cosmic inhomogeneities. In the standard model of cosmology the primordial density power spectrum is taken to be sub-Poissonian and subsequent non-linear evolutions will inevitably produce white noise which will dominate on the largest scales. Non-observation of white noise on the Hubble scale precludes a power law extrapolation of the power spectrum below one comoving parsec and places severe constraints on a wide variety of phenomena in the early universe, including phase transitions, vorticity and gravitational radiation.