Next Generation Quantum Algorithms for Simulation and Machine Learning

我的建议的主要目的是确定为模拟化学和机器学习的量子计算机提供实际量子优势所需的最小资源。我的目标是通过构建一个统一的框架来实现这一目标，该框架允许随机模拟方法与其他最先进的确定性方法相结合，以更好地近似量子动力学。此外，我将开发严格的方法来模拟量子系统中的量子电动力学，这些方法限制了必须调用提供哈密顿矩阵元素（产生系统能量的矩阵）的子程序来执行模拟的次数。我将进一步开发一个新的量子系统深度学习模型，通过使用量子生成预训练来容忍纠缠并避免梯度衰减。这项工作将由至少两名研究生支持，他们将在多伦多大学招募和培训，并将与工业界（b谷歌）以及学术界（华盛顿大学和悉尼科技大学）的研究人员密切合作。

The main aim of my proposal is to determine the minimal resources needed to provide a practical quantum advantage for quantum computers for simulation of chemistry and machine learning. I aim to achieve this by constructing a unified framework that allows stochastic simulation methods to be combined with other state of the art deterministic methods to better approximate quantum dynamics. Further, I will develop rigorous methods for simulating quantum electrodynamics in quantum systems that bounds the number of times a subroutine that provides the matrix elements of the Hamiltonian (the matrix that yields the energy of a system) must be called to perform the simulation. I will further develop a new model for deep learning for quantum systems that tolerates entanglement and avoids gradient decay by using quantum generative pre-training. This work will be supported by a minimum of two graduate students who will be recruited and trained at the University of Toronto and will involve close collaboration with researchers within industry (Google) as well as academia (University of Washington and the University of Technology Sydney).