Theory Seminar: Quantum Walks and simulation of physical theories

Andreu Anglés-Castillo (Unversity of Valencia)
In this talk I will introduce the basic notions of quantum walks (QW)

Andreu Anglés-Castillo (University of Valencia)
Group seminar (hybrid format: online/seminar room B2.46)
Wed, 17 November 2021, 11:30 am (MEZ)

Abstract:

In this talk I will introduce the basic notions of quantum walks (QW). I will present their analogy with the classical random walk, discuss the properties that they present and why quantum walks may present an advantage over their classical counterpart. I will explore some of their applications in algorithms and briefly discuss their polynomial speedup on some quantum algorithms. Then I will move on to the main part of the talk, which is their use in simulation of physical theories. I will discuss their continuum limit and how, in the simplest case, the Dirac equation is recovered. Then we will explore a broader class of quantum walks and their use in two main theories. First, we examine a case where the QW is subject to temporal noise, and how this model can recover, in the continuum limit, Lindbladian dynamics. Secondly, I will briefly discuss the ingredients necessary for a QW to be able to reproduce the dynamics of spinors in curved space time. I apply this knowledge to explore a model with 1 extra dimension, the Randall Sundrum model, and examine that the QW reproduces its phenomenology.