Abstract: In this talk, I will give an overview of my current and future research programs as well as discuss a few research results about algorithms, complexity, and quantum many-body physics. The first one is about the so-called Hamiltonian Variational Ansatz, used in Variational Quantum Algorithms for approximating the ground states of condensed matter physics models. The second one is about a Quantum Phase Estimation algorithm based on compressed sensing, which achieves the Heisenberg limit and is suitable for early fault-tolerant quantum computers. Lastly, I will present an SU(2) symmetric semidefinite programming (SDP) hierarchy for the Quantum MaxCut problem, which connects the Heisenberg model in condensed matter physics with optimization algorithms and fundamental computational complexity questions such as the so-called Quantum PCP Conjecture. The talk is going to be rather high level, and no special background in quantum computation or theoretical computer science is assumed.

Bio: Dr. Cunlu Zhou is currently an NSF FRHTP Postdoctoral Fellow at the Center for Quantum Information and Control at the University of New Mexico. He completed his PhD in Mathematics in 2019 at the University of Notre Dame under the supervision of Roxana Smarandache and Leonid Faybusovich. Following his graduation, he undertook a postdoctoral position with Henry Yuen in the Department of Computer Science at the University of Toronto. His research interests lie at the interdisciplinary crossroads of optimization, quantum computing, and quantum many-body physics. They span a broad range of problems from fundamental theoretical questions in computational complexity to the development of efficient practical classical optimization algorithms, as well as near-term and early fault-tolerant quantum algorithms. He is especially interested in questions that explore the fundamental connections between mathematics, computer science, and the physical world.