Joint Statistics and Applied Mathematics Colloquium: Mohammad Mohammadisiahroudi (Lehigh)
quantum computing and optimization
Location
Mathematics/Psychology : 106
Date & Time
February 14, 2025, 12:00 pm – 1:00 pm
Description
Title: Quantum Computing and Optimization: Challenges, Opportunities, and Advances
Abstract: Over the past few decades, quantum computing has evolved from a theoretical concept into a rapidly advancing field with the potential to revolutionize computational science. While significant challenges remain in hardware development, recent advances in quantum algorithms suggest that quantum computing can offer novel approaches to solving complex problems, particularly in mathematical optimization. In this talk, I will explore the intersection of quantum computing and mathematical optimization, beginning with a high-level introduction to the principles of quantum computation and the opportunities it presents. The discussion will focus on how quantum computing can accelerate the solution of computationally hard optimization problems. I will then introduce quantum-enhanced and quantum-inspired optimization methodologies, highlighting their advantages over classical approaches. In particular, I will present my work on quantum and quantum-inspired interior point methods for conic optimization. These methods integrate quantum linear algebra techniques into classical and novel interior point frameworks. Compared to classical methods, these methods exhibit improved computational complexity and scalability with respect to the problem dimension. The major challenges in leveraging quantum computing for optimization are the inherent inexactness of quantum solvers and their sensitivity to problem conditioning. To address these challenges, we developed refined interior point methods, designed to enhance robustness against errors while leveraging quantum speed-up. I will outline the theoretical foundations and complexity advantages of our approach, along with numerical results that provide insights into its performance and scalability.