My interests are theoretically exploring quantum simulation of interesting physical phenomena that are otherwise difficult to simulate. I mainly think about two kinds of platforms for quantum simulation: dilute ultracold gases for analog quantum simulation, and digital quantum algorithms on near-term circuit-based noisy intermediate scale quantum hardware.

 

Analog Quantum Simulation

 

One of the main questions that has driven my research is what phases of matter are possible, and how can we produce them with quantum simulation on ultracold gases? I use tools such as synthetic gauge fields produced from pairs of Raman lasers, optical Feshbach resonances, and synthetic lattices created from internal states of ultracold molecules to achieve these novel phases. In my proposals, I have thought about using such tools to produce various phases of matter, such as topological superconductors, supersolids, Kondo insulators, resonating valence bond states, and quantum strings. These novel phases of matter, despite being predicted theoretically, have often never been observed before. Experimentally creating these phases will lead to rich practical applications. For example, it is predicted that the excitations of topological superconductors can be used to perform topologically protected quantum computing.

 

Digital Quantum Algorithms

 

Recently, my interests have broadened to include quantum simulation on universal quantum computing platforms, such as trapped ions and superconducting circuits. I have been thinking about how we can use these platforms for solving hard optimization problems with an advantage over classical algorithms. I’m also intrigued by the question of what quantum algorithms can exist that provide a speedup over classical algorithms for practical problems, how do we devise them, and for what class of problems? In a recent interdisciplinary collaboration with engineers, mathematicians and computer scientists at Rice University, I developed a quantum counting algorithm to compute the weighted count of ground states of an arbitrary classical spin Hamiltonian. The project was motivated by the important engineering application of finding an upper bound for a network’s reliability.