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Center for Nonlinear Studies |
Computational optimization faces challenging computational tasks that motivate constant research to improve the performance of solution algorithms. Optimization problems, such as those that arise in different areas of Logistics, Engineering, Manufacturing, and Machine Learning, among others, are among these problems. Solving these problems efficiently is essential for addressing important industrial applications and societal challenges.Quantum computers have the potential to efficiently solve challenging computational problems. For optimization, current devices can already implement a type of nonlinear and combinatorial problem. However, available quantum computers cannot yet address practical problems; they are limited to small sizes and do not handle constraints well. In this talk and tutorial, we present the modeling strategy of discrete nonlinear optimization known as Mixed-Integer Nonlinear Programming, explain some of the approaches that quantum computers use to solve Quadratic Unconstrained Binary Optimization (QUBO) problems, and share our contributions to addressing practical optimization problems using quantum computers. We highlight our work on reformulations of MINLP to QUBOs and hybrid classical-quantum algorithms to solve a subclass of MINLP considering constraints and global convergence via decomposition strategies. These strategies rely on breaking the problems down into QUBO subproblems that can be solved by quantum computers and classical routines that ensure robustness and state-of-the-art efficiency. We also highlight how techniques from mathematical programming, such as Bayesian Optimization, can improve quantum algorithms with applications in computational chemistry. Finally, we present recent work on machine learning with privacy guarantees.
Host: Harsha Nagarajan (T-5), Carleton Coffrin (A-1)