Annotation
Can we look at the mathematical shape and chaos of a quantum circuit's landscape before training it, and know immediately if the algorithm is going to learn? In this talk, we answer this question by introducing a novel framework that uses landscape geometry and chaos theory to forecast quantum advantage in Variational Quantum Algorithms (VQAs). Moving away from traditional accuracy benchmarking, we analyse the cost function manifold through two complementary lenses: Spectral Hessian Analysis to map local geometric ruggedness, and Lyapunov Exponents to quantify the chaoticity of optimisation trajectories. Together, these tools diagnose catastrophic training bottlenecks—such as Barren Plateaus and Information Scrambling—at "Epoch Zero." Backed by massive state-vector simulations on the Karolina IT4I HPC cluster, we show how these topological properties serve as predictive indicators of an algorithm's viability. This research establishes a quantitative pipeline to determine problem-to-algorithm suitability, ensuring we deploy quantum resources only where advantage is mathematically viable.
Benefits for the attendees, what they will learn:
- The Takeaway: Attendees will learn how to evaluate the trainability of a variational quantum ansatz before wasting valuable GPU/QPU hours on optimisation loops.
- The Mechanism: Understanding how to use initial state geometry to identify catastrophic bottlenecks like Barren Plateaus and divergence before the first gradient step is ever taken.
Level
Beginner - intermediate
Language
English
Prerequisites
Basic knowledge of quantum mechanics and classical machine learning.
Tutor
Van Binh Henri VU is a quantum algorithms researcher in the Quantum Computing laboratory at the IT4Innovations National Supercomputer Center (IT4I). He received his Ph.D. in condensed matter physics from the University of Paris-Saclay and the French Alternative Energies and Atomic Energy Commission (CEA) in France. He is currently developing quantum computing to tackle real use cases, and he is actively participating in maintaining the wellness of the quantum hardware at IT4I.
Acknowledgements
This course was supported by the Ministry of Education, Youth and Sports of the Czech Republic through the e-INFRA CZ (ID:90254).
All presentations and educational materials of this course are provided under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license.