Model Reduction for Entanglement Routing

Overview

The work will entail: Modeling a quantum network (QN) requires the ability to understand complex system interactions between the noisy environment, the physical components, and the quantum states. Uniform Manifold Approximation and Projection (UMAP) is a leading dimension reduction method, noted for its speed, interpretability, and ability to capture global features. Though UMAP is inspired by sheaf theory, a mathematical framework for relating local and global structures, the algorithm is ultimately framed in terms of weighted graphs. The successful candidate will design and implement an extension to UMAP to capture temporal dynamics and apply the model to experimental measurements of the channel to predict features such as the time-of-flight of photons and entanglement fidelity. The candidate will develop a quantum networking simulation model that can adapt in real-time at sufficient time scales to mitigate entanglement distribution errors.

Qualifications

• 2+ years of post-doctorate experience in applied category theory.
• 2+ of experience in the research and development of mathematical foundations for Artificial Intelligence (AI) with sheaf or category theory.
• Familiarity with proof assistants (Lean) and modeling platforms.
• Ability to develop prototypes of tools needed to analyze data.
• Strong oral and written communication skills.

Research Proposal

Key responsibilities will include but are not limited to:

• Assess currently available dimension reduction methods, including UMAP, based on applied category theory.
• Adapt UMAP to capture higher order temporal and spatial relationships.
• Develop a digital twin model of the quantum channel.
• Verify the dimension reduction techniques to extrapolate time-of-flight and entanglement distribution rates.
• Present and write manuscripts describing the above work.