How to find lower bounds to ground state energies

Description

QICI (Quantum Information and Computation Initiative) seminar talk at the University of Hong Kong, Computer Science Department
Abstract:
Computing the ground state energy of a quantum many-body system is a central task in many areas of physics. One of the most commonly used methods is the use of variational ansatz wavefunctions. They yield upper bounds on the true ground state energy, as they restrict the search space from the space of all quantum states to the variational ansatz. But how could we obtain lower bounds -- after all, this requires to enlarge the search space beyond all quantum many-body states? In my talk, I will explain how we can systematically enlarge the search space of quantum states using hierarchies of so-called convex relaxations. Those hierarchies allow to obtain rigorous lower bounds to ground state energies, each level of the hierarchy can be solved efficiently, and the hierarchy converges to the true ground state energy. I will then explain how the performance of such relaxations in the quantum many-body context can be significantly improved using compression schemes which are inspired by renormalization transformations. It will turn out that this naturally gives rise to a renormalization scheme based on so-called tensor networks, which themselves form a powerful class of variational wavefunctions.

Period	19 Dec 2024
Held at	University of Hong Kong, Hong Kong
Degree of Recognition	International