Scientific Series

The theory of quasimaps to Nakajima quiver varieties X has recently been used very effectively by Aganagic, Okounkov and others to study symplectic duality. For certain X, namely Hilbert schemes of ADE surfaces, it turns out quasimap theory is equivalent to a particular flavor of Donaldson-Thomas theory on a related threefold Y. I will explain this equivalence and how it intertwines concepts and tools from the two sides. For example, symplectic duality has something to say about the crepant resolution conjecture for Y.

The astrophysical background of gravitational waves (AGWB) is composed by the incoherent superposition of gravitational wave signals emitted by resolved and unresolved astrophysical sources from the onset of stellar activity until today. In this talk, I  will present a theoretical framework  to characterize the AGWB in terms of energy density and polarization and  I will show predictions for the angular power spectra of the background anisotropy and for its cross-correlations with electromagnetic observables, in the frequency bands accessible by  LIGO/Virgo and  LISA.  I will then discuss the astrophysical content of these observables, give an overview of the state of the art of observations, and highlight future observational challenges.

The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it allows for near-optimal state discrimination. A hurdle to the experimental realization of these vaunted theoretical tools is the lack of a systematic and efficient method to implement them. We rectify this lack using the recently developed tools of quantum singular value transformation and oblivious amplitude amplification, providing a quantum algorithm to implement the Petz recovery channel. Our quantum algorithm also provides a procedure to perform pretty good measurements when given multiple copies of the states that one is trying to distinguish.

Using the same toolbox, we also develop a quantum algorithm for enacting the polar decomposition, a workhorse in linear algebra. This provides an alternative route to implementing a pretty-good measurements for the special case of pure states, which speeds up the general-purpose algorithm developed above.

We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.

Mapping of galaxy density fluctuations on large scales is one of the most important goals of observational cosmology in this decade. These observations can significantly improve our knowledge of the universe, its origins and composition. In this talk I will review some of the science goals of the ongoing and future spectroscopic galaxy surveys and explain how these goals can be met. In particular, I will focus on some recent progress in theoretical modelling of the nonlinear structure formation and show how it can be used to extract cosmology from observations of the cosmic web. As an example I will present several analyses from the publicly available Baryon Oscillation Spectroscopic Survey (BOSS) data and results for the standard LCDM model as well as several relevant extensions.

Hoop conjecture suggests that microscopic black holes can be produced in collisions of high energy particles if the fundamental gravity scale is lowered to the electroweak scale in extra dimension models. This opens up the possibility of studying extra dimensions in collliders and neutrino telescopes. In this talk, I will introduce the unique signatures associated with black holes from cosmic neutrino-nucleon scattering in IceCube-Gen2. These signatures include new topologies, distinct energy distributions and unusual ratios of hadronic-to-electronic energy deposition. I will also discuss the study of dark sector in future colliders through the investigation of the production and decay of microscopic black holes and the implications of these black holes for the early universe.

We construct a minimal theory describing the optical activity of a thin sheet of a twisted material, the simplest example of which is twisted bilayer graphene. We introduce the notion of "twisted electrical conductivity" which parametrizes the parity-odd response of a thin film to a perpendicularly falling electromagnetic wave with wavelength larger than the thickness of the sheet, and relate the chiral response to this kinetic coefficient. We show that the low-frequency Faraday rotation angle has different behaviors in different phases: \omega^2 for insulators and \omega^0 for superconductors. In both cases the frequency dependence of the Faraday rotation angle can be obtained from a simple power counting in an effective field theory. In the metallic state, the twisted conductivity is proportional to the "magnetic helicity" (scalar product of the velocity and the magnetic moment) of the quasiparticle, averaged around the Fermi surface. Many aspects of the theory are general and applicable to strongly correlated phases.

Reference: Dung X. Nguyen and DTS, arXiv:2008.02812.

Majorana zero modes have attracted much interest in recent years because of their promising properties for topological quantum computation. A key question in this regard is how fast two Majoranas can be exchanged giving rise to a unitary gate operation. In this presentation I will first explain that the transport of Majoranas in one-dimensional topological superconductors can be formulated as a “simple” optimal control optimization problem for which we propose several different control regimes. Next I will discuss the optimization methods, Differential Programming and Natural Evolution Strategies, that were applied to the Majorana control problem and came up with a counter-intuitive transport strategy. This strategy, which we dubbed jump-move-jump, will form the focus of the last part of the presentation in which I explain the key underlying mechanisms behind the strategy by reformulating the motion of Majoranas in a moving frame. I will conclude by arguing that these results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems with performance levels that make it relevant to the realization of large-scale quantum technology.

Renormalisation in curved spacetimes is an involved subject. In contrast to renormalisation in a flat spacetime, the standard momentum representation is not directly available. Nevertheless, the momentum dependence of correlation functions is crucial to deciding whether a theory is unitary and causal. I will discuss how to define a notion of momentum dependence in gravity on a fundamental level. With this at hand, one can discuss an important quantum field theory observable: scattering cross sections. Taking the example of gravity-mediated scalar scattering, I will discuss conditions that a quantum field theory of gravity has to fulfil to have a well-behaved scattering amplitude. These can be satisfied without the introduction of massive higher spin modes as is done in string theory. Finally, I will review the status of first principle calculations of the non-perturbative momentum dependence of quantum gravity correlation functions.

A classical result of R. Courant gives an upper bound for the count of nodal domains (connected components of the complement of where a function vanishes) for Dirichlet eigenfunctions on compact planar domains.  This can be generalized to Laplace-Beltrami eigenfunctions on compact surfaces without boundary. When considering random linear combinations of eigenfunctions, one can make this count more precise and pose statistical questions on the geometries appearing amongst the nodal domains: what percentage have one hole? ten holes? what percentage have their boundary being tangent 100 times to a fixed non-zero vector field? The first 20-25 minutes will give a survey on some fundamental results of Nazarov-Sodin, Sarnak-Wigman, and Gayet-Welschinger before presenting some joint works with I. Wigman (King's College London) and Matthew de Courcy-Ireland (École Polytechnique Fédérale de Lausanne) answering these questions in the last 25-30 minutes.

Gravitational waves from the coalescence of compact binaries provide a unique opportunity to test gravity in strong field regime. In particular, the postmerger phase of the gravitational signal is a proxy for the nature of the remnant.

This is of particular interest in view of some quantum-gravity models which predict the existence of horizonless dark compact objects that overcome the paradoxes associated to black holes. Such dark compact objects can emit a modified ringdown with respect to the black hole case and late-time gravitational wave echoes as characteristic fingerprints.

In this talk, I develop a generic framework to the study of the ringdown of dark compact objects and provide a gravitational-wave template for the echo signal. Finally, I assess the detectability of dark compact objects with current and future gravitational-wave detectors.

Zero-knowledge proofs are one of the cornerstones of modern cryptography. It is well known that any language in NP admits a zero-knowledge proof. In the quantum setting, it is possible to go beyond NP. Zero-knowledge proofs for QMA have first been studied in a work of Broadbent et al (FOCS'16). There, the authors show that any language in QMA has an (interactive) zero-knowledge proof. In this talk, I will describe an idea, based on quantum teleportation, to remove interaction at the cost of adding an instance-independent preprocessing step. Assuming the Learning With Errors problem is hard for quantum computers, the resulting protocol is a non-interactive zero-knowledge argument for QMA, with a preprocessing step that consists of (i) the generation of a Common Reference String and (ii) a single (instance-independent) quantum message from the verifier to the prover.

This is joint work with Thomas Vidick and Tina Zhang