# IQFA Conference Talk

11 Nov 2016The 7th colloquium of the CNRS GDR Quantum Engineering, Foundations and Applications (IQFA) was held in Telecom ParisTech (Paris), from 16th to 18th November 2016.

Some related links: webpage of the Groupe de Recherche; the 7th IQFA conference webpage; and Quantum Technologies scientific roadmap.

In this conference, I gave an oral presentation of joint work with Pablo Arrighi and Stefano Facchini, *Quantum walking in curved spacetime: $(3+1)$ dimensions, and beyond*.

The slides of the presentation are available here.

This is the abstract of the talk:

A Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation), and thus provide us with discrete toy models of familiar particles (e.g. the electron). We study the continuum limit of a wide class of QWs, and show that it leads to an entire class of PDEs, encompassing the Hamiltonian form of the massive Dirac equation in (3 + 1)-dimensional curved spacetime. Therefore a certain QW, which we make explicit, provides us with a unitary discrete toy model of the electron as a test particle in curved spacetime, in spite of the fixed background lattice. This means that the metric field can be represented by a field of local unitaries over a lattice. Mathematically we have introduced two novel ingredients for taking the continuum limit of a QW, but which apply to any quantum cellular automata : encoding and grouping.