Felipe Montealegre-Mora

Profile

I am a passionate problem solver with a rigorous mathematical formation and ample programming experience. During my PhD I worked on quantum information processing in the group of David Gross at University of Cologne, Germany. From there I moved towards ecological data science and statistics, in Carl Boettiger’s lab at UC Berkeley. Exciting times!

I have worked with a varied portfolio of mathematical techniques and aim to continue expanding it.

In recent months I have been developing data-science solutions to ecological problems. Here I have worked with tools from timeseries forecasting, Bayesian hierarchical models and deep reinforcement learning. The problems we are looking at here range from population distribution modelling and forecasting to fishery and natural resource management. There’s many interesting projects in the making right now!

Throughout grad school I worked at the interface of representation theory and quantum computing. My work spanned from abstract algebra, to algorithm development and coding.

I studied the representation theory of the Clifford group and the geometry of the stabilizer polytope. My main focus here was on stabilizer tensor powers—a ubiquitous object within the theory of quantum fault tolerance. My work drew bridges between quantum error correction and the mathematical field of Howe duality. These connections have opened up possibilities for interdisciplinary fertilization and collaboration. Moreover, this work lead to a novel method for efficiently generating unitary t-designs with Clifford-dominated quantum circuits. This is a key development: on the one hand, t-designs are an exceedingly useful practical tool in a myriad of areas—e.g. quantum cryptography, randomized benchmarking and many-body quantum system modelling—, and on the other, Clifford circuits are efficiently simulatable classically and rather well-behaved algebraicly.

During my PhD I also worked on numerical representation theory. Namely, together with my collaborators, we created a software suite (RepLAB) which heuristically decomposes compact group representations. The suite is geared towards dimensional-reduction applications in convex optimization problems, allowing the researcher to obtain the symmetrized optimization problem directly as an output. While our approach has considerably better runtime than competing algorithms, it does so at the cost of having no guarantee of accuracy. In a follow up project, we developed a certification algorithm which provides this guarantee on RepLAB’s output. 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.