Growing up in the 21st century, I have first-handedly witnessed the extraordinary impact of Moore’s Law scaling on both scientific research and our daily lives. Notable examples include the development of cellular communication, or of big data techniques in research fields such as personalized medicine. As transistor sizes approach the atomic limit, however, this scaling is expected to end soon. This led me to pursue quantum computing, one of the most promising solutions to this upcoming challenge. Quantum computing is an approach to computer science that incorporates the principles of quantum mechanics, such as superposition and entanglement.
Some particular topics I have published papers on include:
During my undergraduate studies, I did research over the course of two summer internships. My first research experience was a 12-week summer research internship under Prof. Luming Duan at Tsinghua’s Institute for Interdisciplinary Information Sciences in the summer of 2015, after my sophomore year. During that summer, I studied potential applications in which quantum computers could solve problems exponentially faster than classical computers. In particular, after reading lots of textbooks on quantum computing and classical machine learning, I published my first paper providing a quantum algorithm to exponentially speed up a classical machine learning technique called discriminant analysis.
Topological quantum computation
For the summer after my junior year, I decided to continue in quantum computing, but I wanted to explore some of the more mathematical and physical aspects. This led me to apply for a summer research internship at Microsoft Station Q, UCSB, a group with many world-class mathematicians and condensed matter physicists working on topological quantum computation (TQC). TQC is a paradigm to encode quantum information in the topological degrees of freedom in certain systems. This protects the information from local decoherence, one of the biggest challenges to current development of quantum computers. (Mathematically, topological properties are global properties that survive under local deformations; physically, topological degrees of freedom in quantum systems are degrees of freedom that are robust under local perturbations of the system).
Traditionally, TQC has been mathematically developed using anyons, which are point-like, quasi-particle excitations in the bulk of topological phases of matter (e.g., Fractional Quantum Hall systems). In principle, one possible mathematical theory of anyons exists for each finite group (and more generally, for each unitary fusion category). Universal gate sets for quantum computing have been developed theoretically from some of these mathematical models, but unfortunately, they require physical systems (non-abelian phases) that are extremely difficult to realize experimentally (if at all possible). My research at Station Q tackles this problem by proposing ways to “engineer” the computationally powerful, non-abelian objects from easy to realize, abelian phases: in particular, we do this by examining boundaries of the non-abelian phase (gapped boundaries).
In a series of three papers, we first develop mathematical and physical models to study gapped boundaries in complete generality (CMP paper). We then study what happens when different gapped boundaries meet at a point, forming a boundary defect: in our PRB paper, we study various topological properties of these defects, and the interesting physics that they give rise to. Finally, in our PRL paper, we present our solution to obtain a universal TQC gate set using gapped boundaries of an easily realized abelian phase: the bilayer fractional quantum Hall 1/3 state (mathematically known as D(Z3)).