FET: Fundamentals of Quantum Boltzmann Machines

Modern society increasingly relies on the ability to analyze complex data, from improving medical research to strengthening secure communication and advancing emerging technologies. This project focuses on developing new methods for machine learning that operate using the principles of quantum physics, an area expected to play a major role in future computing systems. While current approaches to quantum machine learning face significant limitations, there is a promising but underexplored framework known as quantum Boltzmann machines that may overcome some of these challenges. By establishing a deeper understanding of how these models work and when they are most effective, this project aims to expand the range of problems that advanced computing systems can address. The outcomes have the potential to benefit science and engineering broadly, support the development of a skilled and diverse workforce, and contribute to national priorities in innovation, economic competitiveness, and secure information technologies. This project develops the theoretical foundations of quantum Boltzmann machines as a framework for quantum machine learning. The research investigates several core questions, including the conditions under which these models avoid training difficulties observed in other quantum approaches, the design of quantum analogs of established training algorithms, and the extension of generative modeling techniques to fully exploit both hidden and visible components of the model. Additional efforts examine the relationship between quantum Boltzmann machines and tensor network methods, as well as the performance of advanced optimization techniques such as second-order methods and natural gradient descent. The project employs tools from quantum information theory, optimization, and machine learning theory to analyze convergence properties, representational capabilities, and computational efficiency. The anticipated contributions include new theoretical insights, improved training methodologies, and a clearer understanding of the role these models can play in advancing quantum machine learning. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2611810 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Mark Wilde | Institution: Cornell University, ITHACA, NY | Award Amount: $758,998 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2611810 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2611810.html