Talks

"One of the central challenges in quantum information science is to design quantum algorithms that outperform their classical counterparts in combinatorial optimization. In this talk, I will describe a modification of the quantum adiabatic algorithm (QAA) [1] that achieves a Grover-type speedup in solving a wide class of combinatorial optimization problem instances. The speedup is obtained over classical Markov chain algorithms including simulated annealing, parallel tempering, and quantum Monte Carlo. I will then introduce a framework to predict the relative performance of the standard QAA and classical Markov chain algorithms, and show problem instances with quantum speedup and slowdown. Finally, I will apply this framework to interpret results from a recent Rydberg atom array experiment [2], which suggest a superlinear speedup in solving the Maximum Independent Set problem on unit-disk graphs. [1] Farhi et al. (2001) Science 292, 5516 [2] Ebadi et al. (2022) Science 376, 6598"

In this talk, I will introduce the so-called entanglement linear response, i.e., response under entanglement generated unitary dynamics. As an application, I will show how it can be applied to certain anomalies in 1D CFTs. Moreover, I will apply it to extract the quantum Hall conductance from a wavefunction and how it embraces a previous work on the chiral central charge. This gives a new connection between entanglement, anomaly and topological response. If time permits, I will also talk about how it inspires some generalizations of the real-space Chern number formula in free fermion systems.

Zoom link:  https://pitp.zoom.us/j/96535214681?pwd=MldXRkRjZ1J6WS95WXQ0cG03cWdCZz09

Neural networks offer a novel approach to represent wave functions for solving quantum many-body problems. But what kinds of quantum states are efficiently represented by neural networks? In this talk, we will discuss entanglement properties of an ensemble of neural network states represented by random restricted Boltzmann machines. Phases with distinct entanglement features are identified and characterized. In particular, for certain parameters, we will show that these neural network states can look typical in their entanglement profile while still being distinguishable from a typical state by their fractal dimensions. The obtained phase diagrams may help inform the initialization of neural network ansatzes for future computational tasks.

Zoom link:  https://pitp.zoom.us/j/94316902357?pwd=RGxWYm9EWGtGYzBvUzM5ZWdwVTB5dz09

The Deligne-Mumford moduli space of genus 0 curves plays many roles in representation theory.  For example, the fundamental group of its real locus is the cactus group which acts on tensor products of crystals.

I will discuss a variant on this space which parametrizes "cactus flower curves".  The fundamental group of the real locus of this space is the virtual cactus group.  This moduli space of cactus flower curves is also the parameter space for inhomogeneous Gaudin algebras.

Zoom link:  https://pitp.zoom.us/j/96658223425?pwd=NUxRN2FsdWJ1SWtHMlRDcTdHMGNPQT09

In this talk, I will describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced by Fortin and Skiba (DOI:10.1007/JHEP06(2020)028). To begin with, I will give some background on the formalism. In particular, I will map out how to build two-, three-, and four-point functions within this framework. I will then lay out how to construct tensorial generalizations of the well-known scalar four-point blocks for symmetric traceless exchange. As I will discuss, these generalized objects satisfy a number of contiguous relations. Together, these empower us to fully contract the four-point tensorial blocks, ultimately yielding finite spin-independent linear combinations of four-point scalar blocks potentially acted upon by first-order differential operators. I will next proceed to describe how to set up the conformal bootstrap equations directly in the embedding space. I will begin by mapping out a general strategy for counting the number of independent tensor structures, which leads to a simple path to generating the bootstrap equations. I will then examine how to implement this method to construct the two-point, three-point, and ultimately four-point conformal bootstrap equations. Lastly, I will illustrate this method in the context of a simple example.

Zoom link:  https://pitp.zoom.us/j/98920533892?pwd=cDQvOExJWnBsUWNpZml5S1cxb0FJQT09

Many topological phases of lattice systems display quantized responses to lattice defects. Notably, 2D insulators with C_n lattice rotation symmetry hosts a response where disclination defects bind fractional charge. In this talk, I will show that the underlying physics of the disclination-charge response can be understood via a theory of continuum fermions with an enlarged SO(2) rotation symmetry. This interpretation maps the response of lattice fermions to disclinations onto the response of continuum fermions to spatial curvature. Additionally, in 3D, the response of continuum fermions to spatial curvature predicts a new type of lattice response where disclination lines host a quantized polarization. This disclination-polarization response defines a new class of topological crystalline insulator that can be realized in lattice models. In total, these results show that continuum theories with spatial curvature provide novel insights into the universal features of topological lattice systems. In total, these results show that theories with spatial curvature provide novel insights into the universal features of topological lattice systems.

Zoom link:  https://pitp.zoom.us/j/97325013281?pwd=MU5tdFYzTFljMGdaelZtNjJqbmRPZz09

As was realized by Bondi, Metzner, van der Burg, and Sachs (BMS), the symmetry group of asymptotic infinity is not the Poincaré group, but an infinite-dimensional group called the BMS group. Because of this, understanding the BMS frame of the gravitational waves produced by numerical relativity is crucial for ensuring that analyses on such waveforms and comparisons with other waveform models are performed properly. Up until now, however, the BMS frame of numerical waveforms has not been thoroughly examined, largely because the necessary tools have not existed. In this talk, I will highlight new methods that have led to improved numerical waveforms; specifically, I will explain what the gravitational memory effect is and how it has recently been resolved in numerical relativity. Following this, I will then illustrate how we fix the BMS frame of numerical waveforms to perform much more accurate comparisons with either quasi-normal mode or post-Newtonian models. Last, I will briefly highlight  some exciting results that this work has enabled, such as building memory-containing surrogate models and finding nonlinearities in black hole ringdowns.

Zoom Link:  https://pitp.zoom.us/j/96739417230?pwd=Tm00eHhxNzRaOEQvaGNzTE85Z1ZJdz09

The usual quantum mechanical description of measurements, unitary kicks, and other local operations has the potential to produce pathological causality violations in the relativistic setting of quantum field theory (QFT). While there are some operations that do not violate causality, those that do cannot be physically realisable. For local observables in QFT it is an open question whether the projection postulate, or more specifically the associated ideal measurement operation, is consistent with causality, and hence whether it is physically realisable in principle.

In this talk I will recap a criteria that distinguishes causal and acausal operations in real scalar QFT. I will then focus on operations constructed from smeared field operators - the basic local observables of the theory. For this simple class of operations we can write down a more practical causality criteria. With this we find that, under certain assumptions - such as there being a continuum spacetime - ideal measurements of smeared fields are acausal, despite prior heuristic arguments to the contrary. For a discrete spacetime (e.g. a causal set), however, one can evade this result in a ‘natural’ way, and thus uphold causality while retaining the projection postulate.

Zoom link:  https://pitp.zoom.us/j/94464896161?pwd=UkhPQnJONmlxYy9pQXJINThpY3l4QT09