Second order necessary conditions for quantum stochastic optimal control problems

TL;DR

This paper develops second order necessary conditions for optimal control in quantum stochastic systems, providing a theoretical foundation for quantum control optimization involving systems driven by fermionic Brownian motion.

Contribution

It introduces second order necessary conditions for quantum stochastic control problems with controls affecting both drift and diffusion, extending classical stochastic control methods to quantum systems.

Findings

Established second order necessary conditions for quantum stochastic control.

Applied variational approach to systems driven by fermionic Brownian motion.

Provides theoretical basis for future quantum control optimization applications.

Abstract

This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum stochastic differential equations driven by fermionic Brownian motion, where the control enters both the drift and diffusion terms. This result provides a theoretical foundation for further exploration of optimization problems and their practical applications in the field of quantum stochastic control.