Quantum Optimal Transport: Bridging Mathematical Foundations and Quantum Information Science

The Department of Mathematics is pleased to welcom Peixue Wu for his talk titled, "Quantum Optimal Transport: Bridging Mathematical Foundations and Quantum Information Science."

Bio: Peixue Wu is a postdoctoral fellow at the Institute for Quantum Computing (IQC) at the University of Waterloo. He received his Ph.D. in mathematics from the University of Illinois Urbana–Champaign in 2023. His research lies at the intersection of quantum information theory, operator algebras and noncommutative analysis.

Abstract: The rapid evolution of Quantum Information Science (QIS) presents new opportunities for mathematical discovery. In this talk, I will explore the framework of quantum optimal transport, demonstrating how it builds up the foundations of QIS and how practical quantum problems inspire new noncommutative structures and mathematical theorems.

The presentation will cover three key advances. First, I will discuss how quantum optimal transport yields a natural finite-dimensional notion of quantum complexity, capturing the transport “cost” of transforming quantum states under physically motivated constraints. Second, positioning the quantum Wasserstein distance as a core metric, I will demonstrate its application to quantum simulations for open systems, deriving the fundamental limits and performance guarantees of these protocols. Finally, I will present a generalization of this theory to the infinite-dimensional setting of von Neumann algebras and discuss how this algebraic framework applies to Quantum Field Theory.