PhD Proposal: Optimization Problems in Quantum Machine Learning

Xuchen You
12.03.2021 09:00 to 11:00

IRB 4107

Quantum computing is promising in providing speed-up in many areas, including numerical analysis, physical simulation, and in particular in machine learning. Recent progress in near-term intermediate-size noisy quantum machines (NISQ) makes variational quantum algorithms (VQA) a strong candidate for demonstrating quantum advantage. VQA finds application in a wide range of tasks including eigendecomposition (variational quantum eigensolver) and machine learning (quantum neural networks). Lately, there has also been much progress in general quantum algorithms for optimization and machine learning with provable speed-ups.Optimization takes a central position both in understanding the potential advantage of VQA and in devising new general quantum algorithms for machine learning. We present our results on hardness and convergence theory for optimization of VQA, characterizing the behavior of VQAs when under-parameterized and over-parameterized. The hardness result suggests that there is not a single under-parameterized variational circuit that can enjoy good optimization landscapes for all problem instances; the convergence result reveals that when the circuit is compatible with the problem, the number of parameters required for fast convergence can be significantly reduced. This motivates our proposal on systematically studying the pruning methods in quantum variational circuits. For general quantum algorithms, we start by presenting a quantum algorithm for pure exploration in multi-arm bandit; we also present a plan for characterizing possible quantum speed-up in optimization.Examining Committee:

Chair:Department Representative:Members:

Dr. Xiaodi Wu Dr. Furong Huang Dr. Soheil Feizi