A Quantum Optimal Control Problem with State Constrained Preserving Coherence

TL;DR

This paper formulates and solves a quantum optimal control problem aiming to maximize fidelity while maintaining decoherence within bounds, using Pontryagin's Maximum Principle for a three-level atom with Markovian decoherence.

Contribution

It introduces a novel quantum control framework with state constraints to preserve coherence, applying Pontryagin's Maximum Principle for the first time in this context.

Findings

Derivation of optimal control conditions for quantum state fidelity

Application to a three-level atom with Markovian decoherence

Complete set of relations for computing optimal controls

Abstract

In this work, we address the problem of maximizing fidelity in a quantum state transformation process controlled in such a way as to keep decoherence within given bounds. We consider a three-level $\Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We introduce fidelity as the performance index for the quantum state transformation process since the goal is to maximize the similarity of the final state density operator with the one of the desired target state. We formulate the quantum optimal control problem with state constraints where the later reflect the fact that the decoherence level remains within a pre-defined bound. Optimality conditions in the form of a Maximum Principle of Pontryagin in Gamkrelidze's form are given. These provide a complete set of relations enabling the computation of the optimal control strategy. This is a novel approach in the context of quantum systems.