Talks

With the race for quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum circuit. While such "supervised quantum models" are sometimes called "quantum neural networks", their mathematical structure reveals that they are in fact kernel methods with kernels that measure the distance between data embedded into quantum states. This talk gives an informal overview of the link, and discusses the far-reaching consequences for quantum machine learning.

Detecting ultralight axion dark matter has recently become one of the benchmark goals of future direct detection experiments. I will discuss a new idea to detect such particles whose mass is well below the micro-eV scale, corresponding to Compton wavelengths much greater than the typical size of tabletop experiments. The approach involves detecting axion-induced transitions between two quasi-degenerate resonant modes of a superconducting accelerator cavity. Compared to more traditional setups, the sensitivity is parametrically enhanced for ultralight axions, allowing for the exploration of vast new areas of parameter space relevant to the QCD axion and astrophysically long-ranged fuzzy dark matter.

The issue of whether quantum effects can affect gravity at cosmological distances still lacks a fundamental understanding, but there are indications of a non-trivial gravitational infrared dynamics. This possibility is appealing for building alternatives to the standard cosmological model and explaining the accelerated expansion of the Universe. In this talk I will discuss some large scale modifications of general relativity due to nonlocal terms, which are assumed to arise at the level of quantum effective action. Nonlocality is a general feature of quantum effective actions for theories with massless degrees of freedom and dynamical mass generation is a typical non-perturbative IR effect. Among several models, cosmological requirements select a single structure of the nonlocal term describing a mass for the conformal mode of the metric. The model fits very well cosmological data and has strong signatures in the tensor sector that could be tested in the future by gravitational-wave detections.

Since their first discovery in 2015, gravitational-wave observations yielded several "surprises." The LIGO and Virgo observatories detected more and heavier black holes than anticipated; the first object in the lower mass gap was found; and LIGO announced the discovery of a particularly heavy black hole that could have not come from stellar core collapse. The surprises point to the possibility that some of LIGO/Virgo's black hole mergers occurred in the dense accretion disks of active galactic nuclei (AGNs). AGNs act like black hole assembly lines, resulting in multiple consecutive mergers that create heavier and faster-spinning black holes. I will discuss what we currently know about AGN-assisted mergers and which of LIGO/Virgo's events are suspects. I will finally discuss the prospects of multi-messenger observations from AGN assisted mergers.

Zoom Link: https://pitp.zoom.us/j/93121526365?pwd=c1VCTjBEZnlXYk5HVTFObVBadHlxQT09

In her Perimeter Institute public lecture, premiering May 12, mathematician Emily Riehl will invite viewers to consider what might be called the “matchmaker’s dilemma.”   

Imagine a matchmaker who wishes to arrange opposite-sex marriages in a dating pool of single men and single women (there’s a mathematical reason for the heteronormative framework, which will be explained). 

The matchmaker’s goal is to pair every man and woman off into couples that will form happy, stable marriages – so perfectly matched that nobody would rather run off with someone from a different pairing. 

In the real world, things don’t work out so nicely. But could they work out like that if the matchmaker had a computer algorithm to calculate every single factor of compatibility? 

In her talk, recorded as part of the Perimeter Institute Public Lecture Series, Riehl will examine that question, its sexist implications, an algorithmic solution, and real-world applications. 

An associate professor of mathematics at Johns Hopkins University, Riehl has published more than 20 papers and two books on higher category theory and homotopy theory. She studied at Harvard and Cambridge and earned her PhD at the University of Chicago.  

In addition to her research, Riehl is active in promoting access to the world of mathematics. She is a co-founder of Spectra: the Association for LGBT Mathematicians, and has presented on mathematical proof and queer epistemology as part of several conferences and lecture series. 

In recent years, random quantum circuits have played a central role in the theory of quantum computation. Much of this prominence is due to recent random quantum circuit sampling experiments which have constituted the first claims of "quantum supremacy".   While random quantum circuits enjoy certain advantages that make them ideal for implementation by near-term quantum experiments, it is unclear a priori why they should be difficult to simulate classically. While we know several examples of quantum algorithms which attain exponential speedups over classical computation, they all seem to rely on highly structured circuits (such as quantum Fourier transforms) which are far from typical. Why then should we expect a generic quantum circuit to realize a large computational advantage?

In this talk we will explain the complexity theoretic basis for the classical hardness of random circuit sampling.

This talk will be based on joint work with Adam Bouland, Chinmay Nirkhe, and Umesh Vazirani (https://arxiv.org/abs/1803.04402), as well as Adam Bouland, Yunchao Liu and Zeph Landau (https://arxiv.org/abs/2102.01738).

Zoom Link: https://pitp.zoom.us/j/92408058752?pwd=b1JoeTVISlpjaXk3ZjBoSi9pYjNUZz09

The power of quantum information lies in its capacity to be non-local, encoded in correlations among entangled particles.  Yet our ability to produce, understand, and exploit such correlations is hampered by the fact that the interactions between particles are ordinarily local.  I will report on experiments in which we use light to engineer non-local interactions among cold atoms, with photons acting as messengers conveying information between them.  We program the spin-spin couplings in an array of atomic ensembles by tailoring the frequency spectrum of an optical control field.  We harness this programmability to access interaction graphs conducive to frustration and to explore quantum spin dynamics in exotic geometries and topologies.  More broadly, advances in optical control of interactions open new opportunities in areas ranging from quantum technologies to fundamental physics.  I will touch on implications for quantum-enhanced sensing, combinatorial optimization, and simulating quantum gravity.

Crossing symmetry asserts that particles are indistinguishable from anti-particles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that probabilities for observing the two scenarios in a scattering experiment are described by one and the same function. Why could we expect it to be true? In this talk we examine this question in a simplified setup and take steps towards illuminating a possible physical interpretation of crossing symmetry. To be more concrete, we consider planar scattering amplitudes involving any number of particles with arbitrary spins and masses to all loop orders in perturbation theory. We show that by deformations of the external momenta, one can smoothly interpolate between the future and the past lightcones without encountering any singularities.

Inflation generically predicts a background of primordial gravitational waves, which generate a primordial B-mode component in the polarization of the cosmic microwave background (CMB). The measurement of such a B-mode signature would lend significant support to the paradigm of inflation. Observed B modes also contain a component from the gravitational lensing of primordial E modes, which can obscure the measurement of the primordial B modes. We reduce the sample variance in the BB spectrum contributed from this lensing component by a process called 'delensing.' In this talk, I will show results from the first demonstration in an improved constraint on primordial gravitational waves with delensing using data from BICEP/Keck, the South Pole Telescope (SPT), and Planck. In addition, I will provide an outlook of joint-analysis efforts of the BICEP/Keck and the SPT collaborations (the South Pole Observatory) to constrain primordial gravitational waves. 

Classical probabilistic models of quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources for information processing tasks.  A common feature of these models is the presence of inaccessible information, as captured by the concept of preparation contextuality:  There are ensembles of quantum states described by the same density operator, and hence operationally indistinguishable, and yet in any probabilistic (ontological) model, they should be described by distinct probability distributions.  In this talk, I discuss a method for quantifying this inaccessible information and present a family of lower bounds on this quantity in terms of experimentally measurable quantities. These bounds, which can also be interpreted as a new class of robust non-contextuality inequalities, are obtained based on a family of guessing games.  As an application of this result, I derive a noise threshold for the presence of contextually in a noisy system, in terms of the average gate fidelity of the noise channel.