Seminar: Hamiltonian Property Testing
By Francisco Escudero Gutiérrez

Francisco Escudero Gutiérrez will give a seminar on Wednesday 04/11 at 2pm in 5A126.

Title: Research Overview and Hamiltonian Property Testing

I will begin by briefly introducing myself, my background, and some of my past research. I will then focus on an ongoing research line to which I have made several contributions: quantum Hamiltonian property testing. Quantum Hamiltonians describe interactions between particles and determine how quantum states evolve over time. The development of quantum devices motivates methods for extracting information about these Hamiltonians through access to the time evolution they generate. Quantum Hamiltonian property testing asks how to distinguish Hamiltonians that satisfy a given property from those that are far from satisfying it. I will present algorithms I have developed for testing whether a Hamiltonian is local or sparse in the Pauli basis, and for testing identity to a specified target Hamiltonian. I will also discuss lower bounds I proved to establish the optimality of these and related algorithms.