Collaborative Research: MATH-DT: Mathematical Foundations of Quantum Digital Twins

This project develops, analyzes, and deploys Quantum Digital Twins (QDTs), which are digital clones of existing quantum computers. Built within a comprehensive mathematical and statistical framework, these QDTs will enable bidirectional interactions between quantum computers and virtual models on classical systems, optimizing quantum performance and marking a significant step toward achieving the proverbial Quantum Leap in computational abilities. This advancement will help maintain the United States' leadership in quantum information science and technology, supporting the National Quantum Initiative Act and producing next-generation quantum-enabled technologies for sensing, information processing, communication, security, and computing. Additionally, the project establishes foundations that can enhance other Digital Twin technologies across various fields, from energy to health. It will also facilitate the interdisciplinary training of young scientists in modern data-driven computational methods and the experimental and theoretical aspects of quantum devices and digital twins, with outreach efforts to local communities and Native American tertiary colleges. The QDTs developed in this project aim to overcome the limitations of traditional quantum simulations, which use a linear component-by-component approach, by introducing four key advancements: (i) the first-ever mathematical formulation of QDTs grounded in a Bayesian probabilistic framework, addressing the inherently probabilistic nature of quantum devices, (ii) new randomized Bayesian experimental design techniques tailored for QDTs, capable of handling the complex dynamics and uncertainties in quantum systems, (iii) a robust generalized Bayesian framework using optimal transportation theory with adaptive prior and model enrichment mechanisms, enabling QDTs to detect and correct their flaws while minimizing system downtime, and (iv) advanced risk-neutral techniques for quantum optimal control and validation, improving QDTs' ability to generate high-fidelity quantum gates. The project also integrates these algorithms and methods into existing open-source software products, demonstrating and disseminating the developed QDTs. 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.