Kinetic Theory: Novel Statistical, Stochastic and Analytical Methods: A numerical methodists adventure in the land of quantum computing
Presenter
October 24, 2025
Keywords:
- Kinetic theory and Stochastic particle systems
- mean field plasma and radiation dynamics
- Boltzmann and Landau type equations and systems
- hydrodynamic limits
- enhanced dissipation
- quasi-neutral limits
- swarming and flocking
- mean-field games
MSC:
- 35Bxx - Qualitative properties of solutions to partial differential equations
- 35Lxx - Hyperbolic equations and hyperbolic systems {For global analysis
- see 58J45}
- 35Q20 - Boltzmann equations {For fluid mechanics
- see 76P05
- for statistical mechanics
- see 82B40
- 82C40
- 82D05}
- 35Q35 - PDEs in connection with fluid mechanics
- 35Q40 - PDEs in connection with quantum mechanics
- 35Q49 - Transport equations {For calculus of variations and optimal control
- see 49Q22
- for fluid mechanics
- see 76F25
- see 82C70
- 82D75
- for operations research
- see 90B06
- for mathematical programming
- see 90C08}
- 35Q70 - PDEs in connection with mechanics of particles and systems of particles
- 35Q82 - PDEs in connection with statistical mechanics
- 35Q83 - Vlasov equations {For statistical mechanics
- 82D75}
- 35Q84 - Fokker-Planck equations {For fluid mechanics
- see 76X05
- 76W05
- see 82C31}
- 35Q89 - PDEs in connection with mean field game theory {For calculus of variations and optimal control
- see 49N80
- for game theory
- see 91A16}
- 35Q91 - PDEs in connection with game theory
- economics
- social and behavioral sciences
- 35Q92 - PDEs in connection with biology
- chemistry and other natural sciences
- 60Gxx - Stochastic processes
- 60Hxx - Stochastic analysis [See also 58J65]
- 70Fxx - Dynamics of a system of particles
- including celestial mechanics
- 70Lxx - Random and stochastic aspects of the mechanics of particles and systems
- 82D05 - Statistical mechanics of gases
- 82D10 - Statistical mechanics of plasmas
Abstract
In this talk we will: 1. Introducing the most basic concepts in quantum computing. 2. Briefly highlight examples of quantum algorithms where the skills of an (numerical) analyst can be of use. 3. Describe one type of quantum computing hardware (a transmon) and how it is modeled. 4. Time permitting, we then turn to the simulation of open quantum systems and show how to design high order accurate methods that exploit low rank structure in the density matrix while respecting the essential structure of the Lindblad equation. Our methods preserve complete positivity and are trace preserving.