CURRENT RESEARCH
In Fall 2022 I am beginning a new collaboration with Achim Kempf (Applied Math) at the University of Waterloo to work on AI and data analysis. Specifically, we are planning to build on prior work by Achim Kempf and collaborators, on how neural networks can learn to utilize correlated auxiliary noise. In this work it is found that neural networks that learn a task on noisy data, such as, e.g. image classification, can simultaneously also learn to improve their performance by exploiting access to separate noise that is correlated with the noise in the data, when such auxiliary correlated noise is available.
In the longer term, our motivation is to explore applying this new approach of ‘Utilizing Correlated Auxiliary Noise’ (UCAN) to one of the main challenges for quantum computing technology, the process of decoherence. Decoherence can be recognized as noise in degrees of freedom in the immediate environment of the physical qubits. The challenge will be to try to access some of those quantum degrees of freedom and to machine-learn, in a UCAN manner, to re-integrate part of the leaked quantum information into the quantum circuit. This could yield a novel form of machine-learned quantum error correction that is not based on traditional quantum error-correction principles such as utilizing redundant coding or topological stability but that instead tries to access environmental degrees of freedom to re-integrate previously leaked quantum information into the circuit. Besides, appealing to quantum neural networks should bring in the further very important advantage that quantum computers can naturally store much more complex noise models than classical computers, because quantum computers can represent noise models in entangled states.
Since the PhD, I have been working on several counting problems regarding connected chord diagrams. Now, in particular, I study diagrams avoiding certain patterns. These still have many unproven connections with a variety of combinatorial structures, including uniquely sorted permutations, lattices, and generalized Catalan paths. This is a collaboration with Lukas Nabergall (UWaterloo) and Alejandro Morales (UMass Amherst).
I do research in the combinatorics of the Wilson-Loop diagrams. This is joint with Karen Yeats (UWaterloo) and Susama Agarwala (Johns Hopkins Applied Physics Lab).
In the Electrical and Computer Engineering Department at UWaterloo, I am working with George Shaker and Omar M. Ramahi on a biomedical engineering project. The project we are working on aims to replace a wearable medical technology called Hexoskin (which reads heart and breathing rates) by an automated radar system. This brings the need for machine learning algorithms to deal with the data comparison and other consequent challenges. I found this a great opportunity to participate in a practical application where one can add and learn, it also offered me the chance to strengthen my machine learning skills.