Next Generation Quantum Algorithms for Simulation and Machine Learning

我的建议的主要目的是确定为量子计算机提供实际量子优势所需的最低资源，以用于化学模拟和机器学习。我的目标是通过构建一个统一的框架来实现这一点，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，以更好地逼近量子动力学。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，以限制必须调用提供哈密顿量(产生系统能量的矩阵)的矩阵元素的子例程来执行模拟的次数。我将进一步开发一个新的量子系统深度学习模型，通过使用量子生成性预训练来容忍纠缠和避免梯度衰变。这项工作将得到至少两名研究生的支持，他们将在多伦多大学招聘和培训，并将与工业界(谷歌)和学术界(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).