Optimal Control of Quantum Systems in Fermion Fields: The Pontryagin-Type Maximum Principle (I)
Abstract
Abstract. In this paper, we derive a Pontryagin-type maximum principle for optimal control of quantum systems in fermion fields. These systems have gained significant prominence in numerous quantum applications ranging from physical chemistry to multidimensional nuclear magnetic resonance experiments. Furthermore, we establish the existence and uniqueness of solutions to backward quantum stochastic differential equations driven by fermion Brownian motion. The application of noncommutative martingale inequalities and the martingale representation theorem enables this achievement.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Aerospace Engineering and Control Systems
Gas Dynamics and Kinetic Theory
Publication details
- Journal / source
- SIAM Journal on Control and Optimization
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 64
- Issue
- 3
- Pages
- 1357–1382
- Publication date
- 14 May 2026
- Language
- EN