CAREER: Uncertainty Quantification for Quantum Computing Algorithms

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This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Quantum computing harnesses properties of quantum states to enable computations that would be intractable using classical computing. It is widely established that, in the future, quantum computing can revolutionize the way one performs and thinks about computation and serve as the backbone of groundbreaking new technologies for scientific discovery, engineering design, national security, and business development, to name a few. Currently, the key barrier in the development of quantum computing is the error induced by the noise in the hardware. The research goal of this project is to develop methods to model the error propagation in quantum computing algorithms and filter the resulting noise in the outcomes. This study will help enhance the performance of general quantum computing algorithms in terms of accuracy and efficiency. The educational goals of this effort are to prepare students for interdisciplinary research and promote STEM participation and equity among underrepresented groups. Outreach activities also involve K-12 students. The investigator will develop new uncertainty quantification methods in the following four directions to understand and alleviate the effect of noise on quantum computing algorithms: (1) describing propagation of gate error and readout error using epistemic uncertainty models; (2) mitigating errors using constrained optimization methods and Bayesian approaches; (3) analyzing asymptotic behavior of the propagation of the error; (4) developing an open-source software package to implement the uncertainty quantification algorithms. These new methods will leverage Bayesian inference approaches, tensor decomposition techniques, asymptotic analysis tools for stochastic differential equations, and high-performance computing packages to build the foundation of a "quantum numerical analysis" framework from a probabilistic perspective. This framework is general, and it can be used to assess the performance of real-world quantum processors and evaluate the suitability of specific quantum computing hardware architectures for a wide range of applications. This project is jointly supported by the Division of Mathematical Sciences: Computational Mathematics Program and the Division of Computing and Communication Foundations: Foundations of Emerging Technologies Program.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.