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, a natural solution to this upcoming challenge.
Some particular topics I have published papers on include:
Quantum algorithms and quantum machine learning
One research area I’ve been particularly interested in recently is the application of near-term quantum processors with ~50-100 or 1000 qubits. While such system sizes are still insufficient for full-blown quantum error correction for tasks such as Shor’s algorithm, it is already promising to consider applications of these devices to the study of quantum many-body physics, where the exponential complexity of many-body systems hinders traditional theoretical or numerical approaches. Motivated by the recent success of machine learning techniques in solving classically complex problems such as image recognition and precision medicine, we believe it is particularly promising to consider the intersection of machine learning and quantum computing approaches for quantum many-body physics.
In our recent Nature Physics paper, we develop a quantum circuit model (QCNN) inspired by classical convolutional neural networks (CNN). We explicitly show the success of our model for two particular applications: (1) Detecting and classifying quantum phases of matter, and (2) Designing and optimizing novel quantum error correction codes. In addition to numerical demonstrations, we are also able to provide theoretical understanding for the underlying mechanism of our model. Furthermore, we provide a protocol for near-term experimental implementation of our method.
I also did research involving quantum algorithms during the summer after my sophomore year as an undergraduate. 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, where 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
Topological quantum computation (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)).