Applied Mathematics Seminar | Leo Zhou, Quantum Computational Advantages in Energy Minimization

QNC 101

Speaker

Leo Zhou, California Institute of Technology

Title

Quantum Computational Advantages in Energy Minimization

Abstract

Finding the minimum of the energy of a many-body system is a fundamental problem in many fields. Although we hope a quantum computer can help us solve this problem faster than classical computers, we have a very limited understanding of where a quantum advantage may be found. In this talk, I will present some recent theoretical advances that shed light on quantum advantages in this domain. First, I describe rigorous analyses of the Quantum Approximate Optimization Algorithm applied to minimizing energies of classical spin glasses. For certain families of spin glasses, we find the QAOA has a quantum advantage over the best known classical algorithms. Second, we study the problem of finding a local minimum of the energy of quantum systems. While local minima are much easier to find than ground states, we show that finding a local minimum under thermal perturbations is computationally hard for classical computers, but easy for quantum computers. These results highlight exciting new directions in leveraging physics-inspired algorithms to achieve quantum advantages in broadly useful problems.