Talks

We present an approach for representing fermionic quantum many-body states using tensor networks, by introducing a change of basis with local unitary gates obtained via compressing fermionic Gaussian states into quantum circuits. These fermionic Gaussian circuits enable efficient disentangling of low-energy states and entanglement renormalization in matrix product states/operators, significantly reducing bond dimension and improving computational efficiency. As a demonstration, we apply this approach to the 1D single impurity Anderson model through suppression of entanglement in both ground states and time-evolved low-lying excited states. We also explore the use of hierarchical compression to generate Gaussian multi-scale entanglement renormalization ansatz (GMERA) circuits and study their emergent coarse-grained physical models in terms of entanglement properties and suitability for time evolution.

Zoom link:  https://pitp.zoom.us/j/99677586832?pwd=ZGdIVGpac3pWcnhJYjlkNU16Wmlndz09

Abstract: TBD

Zoom Link: https://pitp.zoom.us/j/91979071868?pwd=Z0VWSFhJTEJFWkZRbzBtcWdtV0Ezdz09

Tom Leinster recently introduced a curious notion of entropy modulo p (https://arxiv.org/abs/1903.06961). While entropy has a certain meaning in information theory and physics, mathematically it is simply a function with certain properties. Stating these as axioms, the function is unique. Surprisingly, Leinster shows that a function obeying the same axioms can also be found for "probability distributions" over a finite field, and this function is unique too.

In quantum information, mutually unbiased bases is an important set of measurements and an example of a quantum design. While in odd prime power dimensions their construction is based on a finite field, in dimension 2^n it relies on an unpleasant Galois ring. I will replace this ring by length-2 Witt vectors whose arithmetic involves only finite field operations and Leinster's entropy mod 2. This expresses qubit mutually unbiased bases entirely in terms of a finite field and allows deriving an explicit unitary correspondence between them and the affine plane over this field.

Zoom link:  https://pitp.zoom.us/j/94032116379?pwd=TTI1RnByQnFuVHp1MytFUlJxckM4Zz09

Most people are familiar with periodic tessellations and lattices; from the floor in the PI Bistro to their favourite spin systems. In this talk, I will discuss two less familiar families of tessellations and their applications to high energy physics, condensed matter physics, and mathematics: hyperbolic tessellations and quasicrystals. After introducing the basics of regular hyperbolic lattices, I will survey constructions and surprising properties of quasicrystals (like the Penrose tiling), including their classically forbidden symmetries, long-range order, and self-similar structure. Inspired by the AdS/CFT correspondence, I will describe a mathematical relationship between hyperbolic lattices in (D+1)-dimensions and quasicrystals in D-dimensions, as well as the resolution of a conjecture by Bill Thurston. Based on work to appear with Latham Boyle.

Zoom Link: https://pitp.zoom.us/j/91876287518?pwd=NGNLOXZHa1h1cmdnMzJxQzVMVFJJdz09