Efficient Generation of the Triplet Bell State Between Coupled Spins Using Transitionless Quantum Driving and Optimal Control

TL;DR

This paper investigates methods for efficiently generating the triplet Bell state in coupled spins, highlighting limitations of shortcut techniques and proposing optimal control strategies for rapid, high-fidelity state preparation.

Contribution

It analyzes the limitations of transitionless quantum driving and introduces optimal control methods to achieve fast, high-fidelity Bell state generation in coupled spin systems.

Findings

Transitionless quantum driving has fidelity limitations at short times.

Optimal control can generate high-fidelity Bell states in minimal time.

Lower bound on transfer time set by spin interaction strength.

Abstract

We consider a pair of coupled spins with Ising interaction in z-direction and study the problem of generating efficiently the triplet Bell state. We initially analyze the transitionless quantum driving shortcut to adiabaticity method and point out its limitations when the available duration approaches zero. In this short time limit we explicitly calculate the fidelity of the method and find it to be much lower than unity, no matter how large become the available control fields. We find that there is a lower bound on the necessary time to complete this transfer, set by the finite value of the interaction between the spins. We then use numerical optimal control to find bang-bang pulse sequences, as well as, smooth controls, which can generate high levels of the target Bell state in the minimum possible time. The results of the present work are not restricted only to spin systems, but is expected to find also applications in other physical systems which can be modeled as interacting spins, such as, for example, coupled quantum dots.