Quantum Simulation of Diffusion Processes and Applications in Artificial Intelligence

量子计算是备受期待的下一代信息技术。尽管这些计算机在特定计算任务中具有前所未有的计算能力，但设计出比经典的最先进计算更好地执行实际有用和工业相关任务的量子算法仍然是一个重大挑战。在过去的十年中，深度学习已经成为经典计算中的主导技术。然而，这种技术已经达到了极限。例如，为计算机视觉算法提供足够的功率，以将其预测误差减少到其当前值的一半（即，到大约5%的误差）估计造成的二氧化碳排放量相当于整个纽约市一个月的排放量。深度学习还存在其他弱点，这些弱点阻碍了它在许多现实世界场景中的部署，例如，易受安全攻击、依赖于大型数据库以及继承数据中的无意偏差。实现强大的机器智能需要重新思考表征学习的计算基础。在这个项目中，我们将研究量子计算作为实现这一目标的途径。该计划旨在创建用于解决随机和偏微分方程的量子算法。这两种类型的微分方程在科学和工程中有广泛的应用，因为它们被用来模拟各种自然现象，如流体动力学（在天气预报，火箭和飞机的空气动力学等方面的应用），声音、热、弹性、广义相对论和量子力学。在这个程序中特别感兴趣的应用是扩散过程的模拟。这些过程出现在流体和气体的热力学和统计力学建模中，但已应用于许多其他学科（例如，在计算金融中建模股票市场）。此外，模拟扩散过程在训练基于能量的模型中很有意义，这是一种非典型的机器学习模型家族，已被证明可以克服主流深度学习的许多缺点，但依赖于复杂系统的热力学平衡模拟，这对经典计算机来说是一项棘手的任务。克服这一计算瓶颈将释放基于能量的模型的力量，其影响力与深度学习革命本身一样大。我们的课程将让学生接触到物理，数学和计算机科学的广泛领域，包括量子力学，量子计算，统计力学，随机过程，优化和控制，计算复杂性，机器学习和人工智能。学员不仅能够在量子计算领域建立成功的学术生涯，而且将受到量子计算技术部门的高度追捧，以填补量子信息科学家与跨学科技能的正确融合所面临的巨大差距。

Quantum computing is a highly anticipated next generation in information technology. Despite the unprecedented computing power of these computers in select computational tasks, devising quantum algorithms that perform practically useful and industrially relevant tasks better than the classical state-of-the-art computing remains a major challenge. Over the past decade, deep learning has risen as the dominant technique in classical computing. However, this technique is reaching its limits. For example, supplying enough power to computer vision algorithms to reduce their predictive errors to half their current values (i.e., to about 5% error) is estimated to cause as much carbon dioxide emission as the entire New York City does in one month. Deep learning also suffers from other weaknesses that hinder its deployment in many real-world scenarios, e.g., vulnerability to security attacks, dependence on large corpus of data, and inheritance of unintentional biases in the data. Achieving robust machine intelligence requires rethinking the computational foundations of representational learning. In this program we will investigate quantum computation as a path forward to this end. This program aims to create quantum algorithms for solving stochastic and partial differential equations. Both types of differential equations have broad ranges of applications in science and engineering because they are used to model various natural phenomena such as fluid dynamics (with applications in weather forecasting, aerodynamics of rockets and aircrafts, etc.), sound, heat, elasticity, general relativity, and quantum mechanics. The application of particular interest in this program is simulation of diffusion processes. These processes appear in modeling thermodynamics and statistical mechanics of fluids and gases but have been applied to many other disciplines (e.g., modeling stock markets in computational finance). Moreover, simulating diffusion processes is of interest in training energy-based models, an atypical family of machine learning models that have been demonstrated to overcome many shortcomings of mainstream deep learning but rely on simulation of thermodynamic equilibriums of complex systems which is an intractable task for classical computers. Overcoming this computational bottleneck will unleash the power of energy-based models with an impact as large as the deep learning revolution itself. Our program will expose students to a breadth of fields of physics, mathematics, and computer science including quantum mechanics, quantum computation, statistical mechanics, stochastic processes, optimization and control, computational complexity, machine learning, and artificial intelligence. The trainees will not only be able to build successful academic careers in quantum computing but will be highly sought-after by the tech sector in quantum computing to fill the much-felt gap for quantum information scientists with the right blend of interdisciplinary skills.