Search Talks

We consider the problem of certifying entanglement and nonlocality in one-dimensional translation-invariant (TI) infinite systems when just averaged near-neighbor correlators are available. Exploiting the triviality of the marginal problem for 1D TI distributions, we arrive at a practical characterization of the near-neighbor density matrices of multi-separable TI quantum states. This allows us, e.g., to identify a family of separable two-qubit states which only admit entangled TI extensions. For nonlocality detection, we show that, when viewed as a vector in R^n, the set of boxes admitting an infinite TI classical extension forms a polytope, i.e., a convex set defined by a finite number of linear inequalities. Using DMRG, we prove that some of these inequalities can be violated by distant parties conducting identical measurements on an infinite TI quantum state. Both our entanglement witnesses and our Bell inequalities can be used to certify entanglement and nonlocality in large spin chains (namely, finite, and not TI chains) via neutron scattering.

Our attempts at generalizing our results to TI systems in 2D and 3D lead us to the virtually unexplored problem of characterizing the marginal distributions of infinite TI systems in higher dimensions. In this regard, we show that, for random variables which can only take a small number of possible values (namely, bits and trits), the set of nearest (and next-to-nearest) neighbor distributions admitting a 2D TI infinite extension forms a polytope. This allows us to compute exactly the ground state energy per site of any classical nearest-neighbor Ising-type TI Hamiltonian in the infinite square or triangular lattice. Remarkably, some of these results also hold in 3D.

In contrast, when the cardinality of the set of possible values grows (but remaining finite), we show that the marginal nearest-neighbor distributions of 2D TI systems are not described by a polytope or even a semi-algebraic set. Moreover, the problem of computing the exact ground state energy per site of arbitrary 2D TI Hamiltonians is undecidable.

The talk will review the computation of the three point function of gauge-invariant operators in the planar N=4 SYM theory using integrability-based methods. The structure constant can be decomposed, as proposed by Basso, Komatsu and Vieira, in terms of two form-factor-like objects (hexagons). The multiple sums and integrals implied by the hexagon decomposition can be performed in the large-charge limit, and be compared to the results obtained by semiclassics. I will discuss a method to perform these sums and the contributions currently accessible by this approach.

A number of ground based CMB surveys that will survey large fractions of the sky to high sensitivity are currently in the planning stages.  I will give an overview of what can be learned from these surveys about the Universe since recombination, focussing on gravitational lensing science.  I will also discuss some new CMB observables that would be accessible with even more futuristic surveys.

The physics proof of the Atiyah-Singer index theorem relates the Hamiltonian and Lagrangian approaches to quantization of N=1 supersymmetric mechanics. Similar ideas applied to the N=(0,1) supersymmetric sigma model construct two versions of elliptic cohomology: elliptic cohomology at the Tate curve over the integers and the universal elliptic cohomology theory over the complex numbers. Quantization procedures give analytic constructions of wrong-way maps in these cohomology theories. Relating these to the Ando-Hopkins-Strickland-Rezk string orientation of topological modular points to intricate torsion invariants associated with these sigma models. 

Quantum annealing with superconducting qubits: status and prospects
Adrian Lupascu, Institute for Quantum Computing

Quantum-enhanced Gibbs sampling in statistical relational learning
Peter Wittek, Institute of Photonic Sciences, University of Boras

Mathematics can be tasty! It’s a way of thinking, and not just about numbers. Through unexpectedly connected examples from music, juggling, and baking, Dr. Eugenia Cheng will demonstrate that math can be made fun and intriguing for all. Her interactive talk will feature hands-on activities, examples that everyone can relate to, and funny stories. She will present surprisingly high-level mathematics, including some advanced abstract algebra usually only seen by math majors and graduate students. There will be a distinct emphasis on edible examples.