Public Abstract

DE-SC0025101: Quantum Information Science and Koopman Operator Theory for Improved Modeling and Understanding of Plasmas

Award Status: Active

Institution: Trustees of Dartmouth College, Hanover, NH
UEI: EB8ASJBCFER9
DUNS: 041027822

Most Recent Award Date: 08/15/2024
Number of Support Periods: 1
PM: Akli, Kramer

Current Budget Period: 08/01/2024 - 07/31/2025
Current Project Period: 08/01/2024 - 07/31/2027
PI: Giannakis, Dimitrios

Supplement Budget Period: N/A

Public Abstract

Quantum Information Science and Koopman Operator Theory for Improved Modeling and Understanding of Plasmas D. Giannakis, Dartmouth College (Principal Investigator) I. Joseph, Lawrence Livermore National Laboratory (Co-Principal Investigator) J. Slawinska, Dartmouth College (Co-Investigator) Quantum Information Science (QIS) and Fusion Energy Science (FES) promise to deliver radical advances in computational capabilities and access to abundant clean energy, respectively. Yet, realizing these benefits hinges upon overcoming considerable theoretical, methodological, and technical challenges that will require interdisciplinary efforts spanning mathematics, physics, computer science, and engineering. Novel techniques, leveraging operator theory, dynamical systems theory, and data science are needed to consistently and efficiently encode the complex nonlinear dynamics of plasmas into quantum computational algorithms that will open new possibilities in simulation and analysis of fusion energy systems. In response, the overarching goal of this project is to develop an improved mathematical framework and computational techniques for quantum simulation and analysis of plasma dynamics that will provide foundations for successful deployment of QIS to FES applications. Our approach leverages the operator-theoretic formulation of ergodic theory, which represents classical nonlinear dynamics through intrinsically linear Koopman operators on observables, enabling connections between classical and quantum dynamics such as the Koopman-von Neumann formalism. Using this framework, the project will address a hierarchy of problems, focusing on four objectives: (1) Efficient and provably consistent quantum algorithms for chaotic systems; (2) Koopman operator techniques and quantum algorithms for systems with spatial structure governed by partial differential equations (PDEs); (3) Koopman mode identification and model reduction for fluid and kinetic models of plasma dynamics; and (4) Quantum algorithms for closure and subgrid-scale modeling of plasma dynamics. Our algorithms will be suitable for implementation in Noisy Intermediate-Scale Quantum (NISQ) devices, but even if implemented classically they will benefit from structure-preserving properties of quantum mechanical representations of classical dynamics. We will deploy these methods to applications in FES-relevant fluid and kinetic models, including magnetohydrodynamic and Vlasov-Poisson models. The project will contribute towards STEM workforce development through curricular development and training of students and postdoctoral researchers that will take advantage of both University and FFRDC environments.

Quantum Information Science and Koopman Operator Theory for Improved Modeling and Understanding of Plasmas

D. Giannakis, Dartmouth College (Principal Investigator)

I. Joseph, Lawrence Livermore National Laboratory (Co-Principal Investigator)

J. Slawinska, Dartmouth College (Co-Investigator)

Quantum Information Science (QIS) and Fusion Energy Science (FES) promise to deliver radical advances in computational capabilities and access to abundant clean energy, respectively. Yet, realizing these benefits hinges upon overcoming considerable theoretical, methodological, and technical challenges that will require interdisciplinary efforts spanning mathematics, physics, computer science, and engineering. Novel techniques, leveraging operator theory, dynamical systems theory, and data science are needed to consistently and efficiently encode the complex nonlinear dynamics of plasmas into quantum computational algorithms that will open new possibilities in simulation and analysis of fusion energy systems. In response, the overarching goal of this project is to develop an improved mathematical framework and computational techniques for quantum simulation and analysis of plasma dynamics that will provide foundations for successful deployment of QIS to FES applications.

Our approach leverages the operator-theoretic formulation of ergodic theory, which represents classical nonlinear dynamics through intrinsically linear Koopman operators on observables, enabling connections between classical and quantum dynamics such as the Koopman-von Neumann formalism. Using this framework, the project will address a hierarchy of problems, focusing on four objectives: (1) Efficient and provably consistent quantum algorithms for chaotic systems; (2) Koopman operator techniques and quantum algorithms for systems with spatial structure governed by partial differential equations (PDEs); (3) Koopman mode identification and model reduction for fluid and kinetic models of plasma dynamics; and (4) Quantum algorithms for closure and subgrid-scale modeling of plasma dynamics. Our algorithms will be suitable for implementation in Noisy Intermediate-Scale Quantum (NISQ) devices, but even if implemented classically they will benefit from structure-preserving properties of quantum mechanical representations of classical dynamics. We will deploy these methods to applications in FES-relevant fluid and kinetic models, including magnetohydrodynamic and Vlasov-Poisson models. The project will contribute towards STEM workforce development through curricular development and training of students and postdoctoral researchers that will take advantage of both University and FFRDC environments.