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My main research line is to do with quantum inspired data structures in machine learning. Machine learning models of raw audio data suffer from the “curse of dimensionality” in that they need to capture the probability distribution of a time series with a high sampling rate. In quantum mechanics, matrix product states (MPS) have been introduced as a numerical tool for a similar reason. I am currently developing a generative model for audio, based on a MPS description of the time evolution of an open quantum system under continuous measurement. The model structure is analogous to the deep recurrent neural network architecture.
My second line of research is to develop a new variational algorithms based on tensor networks implemented in TensorFlow, to seek the ground state of a quantum system, that should exceed the performance of state-of-the-art methods including DMRG.
I also have a track record studying vortex physics both in high-temperature superconductors and superfluids. In our last work we use numerical and analytical methods to study the ground state of an infinite system of vortex molecules in 2D.
In Plain English
My main research line is to do with borrowing ideas from physics to solve problems in machine learning. More concretely, I am interested in using these ideas to develop a program that can generate new reallistic sound, by just learning from the sound it "hears".
On my second line of research, I am looking into developing new techniques to solve computational problems in a more efficient way.
My previous research is to do with swirls in some special fluids, called superfluids. If you take a glass of water and stir it with a spoon, you find that the water rotates creating a swirl in the middle. A superfluid is a fluid with some special properties. Among others, when you set it under rotation, it creates many swirls instead of just one. Interestingly, these swirls don't decay. Furthermore, under certain experimental conditions that can be tuned in the lab, these vortices appear to be pulled together in bound pairs forming "swirl-molecules". We study the behavior of these molecules.
- Infinite Lattices of Vortex Molecules in Rabi-Coupled Condensates
- Electronic vortex structure of Fe-based superconductors: Application to LiFeAs
- Competing superconducting and magnetic order parameters and field-induced magnetism in electron-doped Ba(Fe1-xCox)2As2