Optimal control of quantum state preparation and entanglement creation in two-qubit quantum system with bounded amplitude

TL;DR

This paper investigates optimal control strategies for quantum state preparation and entanglement creation in a two-qubit system with amplitude constraints, identifying critical times and optimal controls for different objectives.

Contribution

It provides precise critical time points and optimal controls for quantum state and entanglement preparation, improving estimates of quantum speed limits.

Findings

Identified three critical time points for quantum state preparation.

Determined minimal time for maximal entanglement creation.

Derived optimal controls for reaching target states and entanglement levels.

Abstract

We consider the optimal control problem in a two-qubit system with bounded amplitude. Two cases are studied: quantum state preparation and entanglement creation. Cost functions, fidelity and concurrence, are optimized over bang-off controls for different values of the total duration, respectively. For quantum state preparation problem, three critical time points are determined with high precision, and optimal controls are obtained for different durations. A better estimation of the quantum speed limit is obtained, so is the time-optimal control. For entanglement creation problem, two critical time points are determined, one of them is the minimal time to achieve maximal entanglement (unit concurrence) starting from the product state. In addition, the optimal control to reach the unit concurrence is found.