Optimal control of quantum system in fermion fields: Pontryagin-type maximum principle(I)

2024/06/12 by Penghui Wang, Shan Wang, Wang, Penghui +1
Mathematics · Physics and Astronomy · #47C15 #49K27 #81Q93 #81S25 #81V74 #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Probability (math.PR) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2406.08153

openalex publication_date 2024/06/12 · openalex created_date 2024/06/14 · openalex updated_date 2026/07/28

Abstract

In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical chemistry to multi-dimensional 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.

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