Quantum Simulation of Diffusion Processes and Applications in Artificial Intelligence

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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.