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

TL;DR

This paper develops a Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields, addressing existence and uniqueness of solutions to related backward equations using advanced mathematical tools.

Contribution

It introduces a novel maximum principle for fermion field quantum control and proves solution existence and uniqueness for associated backward stochastic equations.

Findings

Established Pontryagin maximum principle for fermion field quantum systems

Proved existence and uniqueness of solutions to backward quantum stochastic differential equations

Applied noncommutative martingale inequalities and martingale representation theorem

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.