Optimal Quantum Control in Fermionic Stochastic Systems With Bounded Delay

This manuscript focuses on the study of optimal quantum control problem for the quantum stochastic model in noncommutative space. The existence and uniqueness of the quantum stochastic differential equation driven by a fermion Brownian motion with bounded delay in finite time interval are established by employing the noncommutative Burkholder–Gundy inequality, generalised Minkowski inequality and generalised Banach fixed‐point theorem. The proposed system is formulated to control the quantum stochastic differential equation and to maximise the probability that the quantum state will reach the target state. By using the Pontryagin maximum principle, optimal quantum control theory is established for the proposed system. Furthermore, an application of the algorithm is presented through numerical simulations which validate the theoretical results.