EAGER: QSA: Solving Optimization Problems on NISQ Computers

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Optimization problems are ubiquitous in all areas of science and engineering. Many important problems in chemistry, physics, and materials science can be cast as the optimization of a cost function under specific constraints. Traditionally, classical numerical optimization methods are the main go-to tool for studying such problems, but these methods are known to be grossly inefficient when tackling problems of this sort due to the exponentially increasing configuration space that needs to be explored. Quantum algorithms — protocols meant to be executed on quantum computers — provide a promising approach to solving such problems. Specifically, hybrid classical-quantum methods have been the focus of much attention in this context recently. The present project seeks to develop and experimentally implement a novel hybrid approach to solving optimization problems that reaches beyond the capabilities of the current state-of-the-art and that enables faster convergence with significantly fewer classical-quantum iterations and considerably fewer repeated experiments per iteration. The developed protocol will in turn allow reaching more accurate solutions to problems as well as the handling of larger problems than allowed by current algorithmic capabilities. One of the main bottlenecks of traditional quantum optimization protocols, such as QAOA and VQE, is that they require many classical-quantum iterations to converge. The main objective of this project is to dramatically reduce the number of classical-quantum iterations. This approach, which relies on combining advanced parametric minimization tools together with recent results in quantum information theory, enables the efficient estimation of physical quantities (observables) with precise control over estimation errors. The present parametric-based minimization is inherently different than state-of-the-art approaches wherein the optimization is based on available data and as such it is expected to substantially reduce the number of classical-quantum iterations. These savings in resources will in turn enhance our ability to solve optimization problems on current NISQ devices. This project is being co-funded by the Division of Chemistry.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.