Felipe Montealegre-Mora

Profile

I am a passionate problem solver with a rigorous mathematical formation and ample programming experience. I recently finished my PhD in the group of David Gross, working on quantum information theory at the University of Cologne. Next stop for me: post-doc on machine learning applied to ecological policy optimization at Berkeley, in the group of Carl Boettiger. 🙂

My grad school research encompassed a number of topics around the interface of representation theory and quantum computing.

I have worked on the representation theory of the Clifford group and the geometry of the stabilizer polytope. These objects are ubiquitous in quantum computing through applications such as error correction, noise characterization, and the simulation of quantum algorithms. My main focus here has been understanding the representation theory of tensor-power representations of the Clifford group and their relation to unitary t-designs and the Theta correspondence. With respect to the latter, in this paper we use methods of quantum error correction to solve an open problem in Howe duality. In this paper we use recent results on the representation theory of the Clifford group to obtain a new method for efficiently generating unitary t-designs.

Moreover I have worked on numerical representation theory. In this paper we introduce an efficient heuristic to decompose numerically-defined representations of compact groups. This method was coded into the Matlab software suite RepLAB. In a follow-up paper, we propose a certification algorithm which guarantees that a given decomposition of the representation is close to exact. I coded this into the Python package RepCert.

Being a firm believer of the democratization of scientific knowledge, I am part of the science communication collective ManyBodyPhysics.