Publication list: See my ArXiv profile or Google Scholar page for the most updated list. My publications are organized below by topic. The descriptions below are organized as most recent first.


Universal quantum computation with group surface codes

It is well-known that the usual surface code does not admit transversal non-Clifford logical operations, which are crucial for universal quantum computation. Among the many approaches to address this problem (such as magic state cultivation and dimension-jumping), one that has received increasing attention of late is code-switching to non-Abelian topological codes (which are based on non-Abelian topological states). Here we study a direct generalization of the surface code to arbitrary finite groups, and discover a rich set of transversal logical gates. In particular, we show that any reversible classical gate on n logical qubits (at arbitrary levels of the Clifford hierarchy) can be performed transversally by switching to an appropriate group surface code. We also develop a generalization of ZX-calculus to the case of finite groups, which enables a circuit implementation of each logical gate. 


Anomaly-based approaches to topological phase transitions

I am also interested in non-perturbative descriptions of quantum phase transitions in unconventional settings. For instance, I have explored 'diabolical critical points', which are examples of topologically protected critical points that curiously do not separate distinct phases of matter. Such critical points can have emergent symmetries and anomalies which constrain the global structure of the surrunding phase diagram. Insights from these questions have led to a deeper understanding of phase transitions in quantum spin liquids. I am also interested in disordered critical points and their detection through correlation functions; recently, we identified the correct correlation functions that show power-law decay in disordered systems with anomaly.


Crystalline topological phases in quantum many-body systems

Crystalline symmetries can endow a topological phase (such as an integer or fractional Chern insulator) with a rich set of additional quantized invariants that do not have any continuum analog. Over the last 20 years, there has been a huge effort to classify (count the number of distinct phases) and characterize crystalline topological states (clarify their underlying mathematical structure, and extract each topological invariant from microscopic models or from experiments). I have worked on various non-perturbative approaches to address these questions, using topological quantum field theory and G-crossed braided tensor category theory in combination with numerics on lattice models. 

This program has uncovered a number of new crystalline invariants in (2+1)-dimensional integer and fractional Chern insulators, including the `discrete shift', a fractionally quantized electric polarization, and additional angular momentum responses. One highlight was to provide a complete characterization of crystalline topological invariants in the square lattice Hofstadter model, a paradigmatic model of Chern insulators. We have also identified fractional analogs of the above invariants in microscopic models of fractional Chern insulators.