High Fidelity Quantum State Transfer by Pontryagin Maximum Principle

TL;DR

This paper develops a control-theoretic approach using Pontryagin's Maximum Principle to optimize quantum state transfer fidelity, providing a systematic way to compute optimal control strategies for quantum systems.

Contribution

It introduces a novel application of Pontryagin's Maximum Principle to quantum state transfer, deriving optimality conditions for maximizing fidelity in quantum dynamics.

Findings

Derived a set of optimality conditions for quantum state transfer.

Provided a framework for computing optimal control strategies.

Enhanced fidelity in quantum state transformation processes.

Abstract

High fidelity quantum state transfer is an essential part of quantum information processing. In this regard, we address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann equation. By introducing fidelity as the performance index, we aim at maximizing the similarity of the final state density operator with the one of the desired target state. Optimality conditions in the form of a Maximum Principle of Pontryagin are given for the matrix-valued dynamic control systems propagating the probability density function. These provide a complete set of relations enabling the computation of the optimal control strategy.