On April 17, as part of its academic seminar series, the Faculty of Physics and Engineering Physics successfully hosted a specialized seminar presented by Nghiem Vu Nhat Anh (Stony Brook University, currently conducting research at Harvard University and soon joining Google Quantum AI). Under the theme “Quantum Algorithms: Applications in Topology, Computational Geometry, and Quantum System Exploration,” the seminar delivered in-depth and up-to-date insights into the field of quantum computing.
At the outset, the speaker highlighted the fundamental motivation driving the field: classical computing systems are approaching their physical limits as device dimensions continue to shrink. In this context, quantum computing emerges as a transformative paradigm, leveraging the principles of quantum mechanics to address challenges that are increasingly intractable for classical approaches.
The core of the seminar focused on the problem of Betti number estimation in Topological Data Analysis (TDA). Beyond the traditional approach based on homology theory, the speaker introduced a novel framework grounded in cohomology - specifically Hodge theory and De Rham cohomology. This perspective enables the analysis of data structures through dual spaces, significantly enhancing the capacity to process and interpret topological information.
Notably, a refined viewpoint was proposed: rather than computing Betti numbers as aggregate quantities, one can track individual homology classes, assess their linear independence, and thereby infer topological features in a more flexible and insightful manner.
The final part of the seminar addressed quantum simulation, a foundational application underpinning many quantum algorithms. In addition to the widely used sparse-access and Linear Combination of Unitaries (LCU) models, the speaker introduced the white-box model, where classical information about the Hamiltonian is explicitly provided. When combined with recent advances in block-encoding techniques, this approach enables highly efficient quantum simulation in a novel framework.
The seminar concluded with an engaging academic discussion, featuring numerous insightful questions from participants. Beyond delivering advanced knowledge, the event fostered research-oriented thinking and inspired students and researchers with an interest in quantum science and technology.
