Scientific Series

We show that specific exponential integrals serve as generating functions of labeled edge-colored graphs. Based on this, we derive asymptotics for the number of edge-colored graphs with arbitrary weights assigned to different vertex structures. The asymptotic behavior is governed by the critical points of a polynomial. As an application, we discuss the Ising model on a random graph and show how its phase transitions arise from our formula.

We explore the interplay of quantum computing and machine learning to advance experimental protocols for observing measurement-induced phase transitions (MIPT) in quantum devices. In particular, we focus on trapped ion monitored circuits and apply the cross entropy benchmark recently introduced by [Li et al., Phys. Rev. Lett. 130, 220404 (2023)], which can mitigate the postselection problem. By doing so, we reduce the number of projective measurements -- the sample complexity required per random circuit realization, which is a critical limiting resource in real devices. Since these projective measurement outcomes form a classical probability distribution, they are suitable for learning with a standard machine learning generative model. In this work, we use a recurrent neural network (RNN) to learn a representation of the measurement record for a native trapped-ion MIPT, and show that using this generative model can substantially reduce the number of measurements required to accurately estimate the cross entropy. This illustrates the potential of combining quantum computing and machine learning to overcome practical challenges in realizing quantum experiments. 

Assuming the polynomial hierarchy is infinite, we prove a sufficient condition for determining if uniform and polynomial size quantum circuits over a non-universal gate set are not efficiently classically simulable in the weak multiplicative sense. Our criterion exploits the fact that subgroups of SL(2; C) are essentially either discrete or dense in SL(2; C). Using our criterion, we give a new proof that both instantaneous quantum polynomial (IQP) circuits and conjugated Clifford circuits (CCCs) afford a quantum advantage. We also prove that both commuting CCCs and CCCs over various fragments of the Clifford group afford a quantum advantage, which settles two questions of Bouland, Fitzsimons, and Koh. Our results imply that circuits made of just U \otimes U-conjugated CZ gates afford a quantum advantage for almost all single-qubit unitaries U.

High temperatures are typically thought to increase disorder. Here we examine this idea in Quantum Field Theory in 2+1 dimensions. For this sake we explore a novel class of tractable models, consisting of nearly-mean-field scalars interacting with critical scalars. We identify UV-complete, local, unitary models in this class and show that symmetry breaking $\mathbb{Z}_2 \to \emptyset$ occurs at any temperature in some regions of the phase diagram. This phenomenon, previously observed in models with fractional dimensions, or in the strict planar limits, or with non-local interactions, is now exhibited in a local, unitary 2+1 dimensional model with a finite number of fields.

The Vera C. Rubin Observatory’s LSST promises unprecedented cosmological constraints, but achieving them requires more than just statistical power—it demands forecasting pipelines that can account for complex astrophysical systematics and modeling challenges on small scales. In this talk, I present work within the LSST Dark Energy Science Collaboration (DESC) to develop a modular forecasting framework that connects realistic data modeling with infrastructure built for extensibility and validation. Drawing on my role as forecasting group lead, I will outline key challenges in pipeline design, the role of validation in maintaining forecast credibility, and the use of good coding practices—such as modularization and model registries—to ensure long-term adaptability. I’ll close with a look at new directions, including forecasts at high redshift and multi-probe combinations, underscoring how thoughtful infrastructure enables reliable science in the LSST era.

Numerical methods are powerful tools for advancing our understanding of quantum gravity. In this talk, I will introduce two complementary numerical approaches. The first focuses on solving nonlinear partial differential equations that arise in Loop Quantum Gravity (LQG)-inspired effective models. This framework enables us to investigate the formation and evolution of shock waves in spherically symmetric gravitational collapse. The second approach involves the use of complex critical points, Lefschetz thimble techniques, and the Metropolis Monte Carlo algorithm to study the Lorentzian path integral in Spinfoam models and Quantum Regge Calculus. These methods offer new insights into quantum cosmology and black-to-white hole transitions.

K-theoretical Coulomb branches are expected to have cluster structure. Cautis and Williams categorified this expectation. In particular, they conjecture (and prove in type A) that the category of perverse coherent sheaves on the affine Grassmannian is a cluster monoidal categorification. We discuss recent progress on this conjecture. In particular, we construct cluster short exact sequences of certain perverse coherent sheaves. We do that by constructing a bridge, relating this (geometric) category to the (algebraic) category of finite dimensional modules over the quantum affine group. This is done by relating both categories to the notion of Feigin--Loktev fusion product.

I will present a unified framework for understanding the statistics and anomalies of excitations—ranging from particles to higher-dimensional objects—in quantum lattice systems. We introduce a general method to compute the quantized statistics of Abelian excitations in arbitrary dimensions via Berry phases of locality-preserving symmetry operations, uncovering novel statistics for membrane excitations. These statistics correspond to quantum anomalies of generalized global symmetries and imply obstructions to gauging, enforcing long-range entanglement. In particular, we show that anomalous higher-form symmetries enforce intrinsic long-range entanglement, meaning that fidelity with any SRE states must exhibit exponential decay, unlike ordinary (0-form) symmetry anomalies. As an application, we identify a new example of (3+1)D mixed-state topological order with fermionic loop excitations, characterized by a breakdown of remote detectability linked to higher-form symmetry anomalies.

The advent of gravitational wave (GW) detections has opened a new window into our understanding of stellar-mass black holes and neutron stars. Ongoing advancements and upcoming third-generation GW detectors are expected to provide increasingly detailed insights into the properties of compact object binaries across cosmic time. In this context, the merger rate density inferred from GW detections can be interpreted as the convolution of the cosmic star formation history, chemical evolution, and binary stellar evolution.
Studying this connection from the perspective of the host galaxies of binary compact objects offers a complementary approach, not only shedding light on the physical conditions that favor different formation channels but also enhancing our ability to interpret GW observations. In this talk, I will discuss two different approaches to modeling the host galaxies of binary compact objects: one based on population synthesis models combined with galaxy catalogs from cosmological simulations, and another based on empirical galaxy scaling relations. I will highlight some of the key results from these models and discuss the next steps where host galaxy properties can provide critical constraints on the origin and evolution of compact object binaries.

Zoom link: https://pitp.zoom.us/j/98089871850

Rydberg atom arrays have emerged as powerful quantum simulators, capable of preparing strongly correlated phases of matter that are potentially challenging to access with classical computational methods. A major focus has been on realizing these arrays on frustrated geometries, aiming to stabilize exotic many-body states like spin liquids. In this talk, I will show how two-dimensional recurrent neural network (RNN) wave functions can be used to study the ground states of Rydberg atom arrays on the kagome lattice. For Hamiltonians previously investigated in this geometry, I will demonstrate that the RNN finds no evidence for exotic spin liquid phases or emergent glassiness. In particular, I will argue that signals of glassy behavior, such as a nonzero Edwards-Anderson order parameter seen in quantum Monte Carlo (QMC) studies, may arise from artifacts related to long autocorrelation times. These results highlight the potential of language model-inspired approaches, like RNNs, for advancing the study of frustrated quantum systems and Rydberg atom physics more broadly.

arXiv paper: https://arxiv.org/pdf/2405.20384

Einstein's theory admits interesting limits with different causal structures obtained by letting the speed of light go to infinity (Galilean or "non-relativistic" limit) or to zero (Carrollian, sometimes called "ultrarelativistic", limit). The Carroll limit turns out to be relevant near spacelike (cosmological) singularities, and particularly so when p-form gauge fields are coupled to gravity as in the context of extended supergravities. The resulting differential equations possess a remarkable interpretation in terms of infinite-dimensional Kac-Moody algebras. The talk will review various aspects of Carroll invariant theories, of the Belinski-Khalatnikov-Lifshitz analysis of spacelike singularities and of the related symmetries.