Format results
Phase diagrams of spin-S Kitaev ladders
Yushao Chen Xanadu Quantum Technologies (Canada)
Wall-crossing structures and Chern-Simons theory.
Yan Soibelman Kansas State University
Deriving the Simplest Gauge-String Duality
Rajesh Gopakumar International Centre for Theoretical Sciences (ICTS)
Quantum Computational Advantage: Recent Progress and Next Steps
Xun Gao Harvard University
Physical Observables in Canonical Quantum Gravity
Axel Maas University of Graz
Probing extreme configurations in binary compact object mergers
Samuel Tootle Goethe University Frankfurt
An asymptotically safe road to quantum gravity with matter
Marc Schiffer Radboud Universiteit Nijmegen
Infinite Dimensional Optimisation Problems in Quantum Information — An operator algebra approach to the NPA Hierarchy
Julius Zeiss Universität zu Köln
The theory of polynomial optimisation considers a polynomial objective function subject to countable many polynomial constraints. In a seminal contribution Navascués, Pironio and Acín (NPA) generalised a previous result from Lassere, allowing for its application in quantum information theory by considering its non-commutative variant. Non-commutative variables are represented as bounded operators on potentially infinite dimensional Hilbert spaces. These infinite-dimensional non-commutative polynomials optimisation (NPO) problems are recast as a complete hierarchy of semidefinite programming (SDP) relaxations by a suitable partitioning of the underlying spaces.
The reformulation into convex optimisation problems allows for numerical analysis. We focus on an operator theoretical approach to the NPA hierarchy and show its equiv-
alence to the original NPA hierarchy. To do so, we introduce the necessary mathematical preliminaries from operator algebra theory and semidefinite programming. We conclude by showing how certain relations on operators translate to SDP relaxations yielding drastically reduced problem sizes.Zoom Link: https://pitp.zoom.us/j/98583295694?pwd=SlcvNG90RzFrODBKSHNaUi84bG9DZz09
TBA
Sandu Popescu University of Bristol
Abstract: TBD
Zoom Link: https://pitp.zoom.us/j/95212522185?pwd=eWx4R3o3cmZISmtPY0xwMmdxc2EzZz09
Phase diagrams of spin-S Kitaev ladders
Yushao Chen Xanadu Quantum Technologies (Canada)
We investigate the ground states of spin-S Kitaev ladders using exact analytical solutions (for S=1/2), perturbation theory, and the density matrix renormalization group (DMRG) method. We find an even-odd effect: in the case of half-integer S, we find phases with spontaneous symmetry breaking (SSB) and symmetry-protected topological (SPT) order; for integer S, we find SSB and trivial paramagnetic phases. We also study the transitions between the various phases; notably, for half-integer S we find a transition between two distinct SPT orders, and for integer S we find unnecessary first order phase transitions within a trivial phase
Zoom link: https://pitp.zoom.us/j/96692976298?pwd=d3dieERwTHJ2MEh5NFF2bFpnS3hOUT09
Wall-crossing structures and Chern-Simons theory.
Yan Soibelman Kansas State University
In 2008 jointly with Maxim Kontsevich we introduced the notion of stability data on graded Lie algebras. In the case of the Lie algebra of vector fields on a symplectic torus it underlies the wall-crossing formulas for Donaldson-Thomas invariants of 3-dimensional Calabi-Yau categories. In 2013 we introduced the notion of wall-crossing structure, which is a locally-constant sheaf of stability data. Wall-crossing structures naturally appear in complex integrable systems, Homological Mirror Symmetry and many other topics not necessarily related to Donaldson-Thomas theory. Recently, in 2020 we introduced a sublass of analytic wall-crossing structures. We formulated a general conjecture that analytic wall-crossing structure gives rise to resurgent (i.e. Borel resummable) series.
Many wall-crossing structures have geometric origin, and moreover they naturally appear in our Holomorphic Floer Theory program. Aim of my talk is to discuss wall-crossing structures associated with a pair of holomorphic Lagrangian submanifolds of a complex symplectic manifold (in most cases it will be the cotangent bundle). These wall-crossing structures underly Cecotti-Vafa wall-crossing formulas, and as such they appear naturally in the study of exponential integrals in finite and infinite dimensions. I am going to explain our conjectural approach to Chern-Simons theory which is based on the idea of wall-crossing structure. In some aspects this approach is related to the work of Witten on analytic continuation of Chern-Simons theory.Zoom link: https://pitp.zoom.us/j/99446428842?pwd=aDRzbFJoNytDNURDUVFMNGQzNjBFQT09
Deriving the Simplest Gauge-String Duality
Rajesh Gopakumar International Centre for Theoretical Sciences (ICTS)
The simplest large N gauge theory is, arguably, the Gaussian matrix (or more generally, one hermitian matrix) integral. We will explicitly show that arbitrary correlators of single trace operators in this theory (without any double scaling limit) are identical to corresponding physical correlators in a dual topological string description. We will present both a novel A-model dual and also a mirror B-model Landau-Ginzburg description. The equality of correlators arises via open-closed-open string triality and a surprising relation to the c=1 string theory. The goal will be, however, to go beyond demonstrating equality but rather to make the duality manifest. For the B-model description this involves Eynard's recasting of topological recursion relations in terms of intersection numbers on moduli space. For the A-model this goes through the relation of Gaussian correlators to the special Belyi covering maps or equivalently, discrete volumes of moduli space. Finally, we also briefly mention the significance of these results for the gauge-string duality of N=4 Super Yang-Mills theory.
Zoom Link: https://pitp.zoom.us/j/93961992131?pwd=MkxlekxWU1ZGbzNZeWpzeU1TMzMrdz09
Quantum Computational Advantage: Recent Progress and Next Steps
Xun Gao Harvard University
This talk is motivated by the question: why do we put so much effort and investment into quantum computing? A short answer is that we expect quantum advantages for practical problems. To achieve this goal, it is essential to reexamine existing experiments and propose new protocols for future quantum advantage experiments. In 2019, Google published a paper in Nature claiming to have achieved quantum computational advantage, also known as quantum supremacy. In this talk, I will explain how they arrived at their claim and its implications. I will also discuss recent theoretical and numerical developments that challenge this claim and reveal fundamental limitations in their approach. Due to these new developments, it is imperative to design the next generation of experiments. I will briefly mention three potential approaches: efficient verifiable quantum advantage, hardware-efficient fault-tolerance, and quantum algorithms on analog devices, including machine learning and combinatorial optimization.
Zoom Link: https://pitp.zoom.us/j/96945612624?pwd=ckRKMFJqZ0Q0dGtFOU91c1hnMzIzZz09
Physical Observables in Canonical Quantum Gravity
Axel Maas University of Graz
Canonical Quantum Gravity can be considered as a gauge theory of translations. Just like in other gauge theories this implies that physical observables need to be gauge-invariant. Hence, quantities like the metric cannot be observables. This poses new challenges, as this requires to rephrase in the quantum theory how to characterize physics. Moreover, such observables are usually composite. To determine them, the Fröhlich-Morchio-Strocchi mechanism from QFT can be borrowed, to have an augmented perturbative approach.
Zoom Link: https://pitp.zoom.us/j/97927004145?pwd=ekFJaUJSc21UUGdkcDZDWCtpSmdIUT09
Probing extreme configurations in binary compact object mergers
Samuel Tootle Goethe University Frankfurt
Numerical relativity continues to play a crucial role in interpreting gravitational wave detections as well as the first multi-messenger detection of GW170817. More so, state-of-the-art models for kilonvae, gravitational waves, and more rely on the thousands of numerical relativity simulations that have taken place over more than 20 years. Simulations of binary systems including neutron stars are particularly taxing due to the equation of state of matter being a significant unknown. In spite of this fact, there exists vast amount of literature on the independent influence mass asymmetry or spin can have on the merger and post-merger dynamics of neutron star binaries across a wide array of possible equations of state.
In this talk I will extend this topic to extremal configurations consisting of binaries that are not only asymmetric, but include appreciable spins on the component neutron stars. To do so I will give an introduction into the initial data problem for numerical relativity, it's complexities, and its importance to current and future research. Furthermore, I will discuss a collection of results for extremal binary configurations including neutron stars and why this line of research is important to enable the next generation of multi-messenger models.
Zoom Link: https://pitp.zoom.us/j/99895521696?pwd=T1VtN0RGbjZrVTNleXB3V0FtQjhldz09
Witnessing non-classicality in a causal structure with three observable variables - Pedro Nobrega Lauand, Physics Institute at University of Campinas
Bell's theorem proves that quantum theory is inconsistent with local physical models and, from the perspective of causal inference, it can be seen as the impossibility of providing a classical causal explanation to quantum correlations. Bell's theorem has propelled research in the foundations of quantum theory and quantum information science. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more complicated causal structures allowing for communication between the parts and involving several independent sources which distribute shares of physical systems in a network. For the case of three observable variables, it is known that there are three non-trivial causal networks. Two of those, are known to give rise to quantum non-classicality: the instrumental and the triangle scenarios. In this talk, we introduce new tools to tackle the compatibility problem in the general framework of Bayesian networks and explore the remaining non-trivial network, which we call the Evans scenario. We do not solve its main open problem –whether quantum non-classical correlations can arise from it – but give a significant step in this direction by proving that post-quantum correlations, analogous to the Popescu-Rohrlich box, do violate the constraints imposed by a classical description of Evans causal structure.
Zoom Link: https://pitp.zoom.us/j/98549320714?pwd=QVllZXNpZTFqekI1ZVUrK3ZLdnRjZz09
An asymptotically safe road to quantum gravity with matter
Marc Schiffer Radboud Universiteit Nijmegen
I will introduce asymptotically safe quantum gravity, which is based on the quantum realization of scale invariance, as one candidate theory to describe nature at all scales. I will discuss the concept of an asymptotically safe fixed point, and how the realization of scale invariance at high energies might provide a predictive and UV-complete description of nature. In particular, I will focus on the interplay of gravity and matter, and highlight mechanisms how this interplay might lead to constraints and predictions of asymptotically safe gravity-matter systems.
Zoom Link: https://pitp.zoom.us/j/99056179498?pwd=SzlXK1R5dExNckFMM1pMS3IvS1VyQT09