Counter-diabatic driving for fast spin control in a two-electron double quantum dot

TL;DR

This paper develops a counter-diabatic driving method for rapid spin control in a two-electron double quantum dot, utilizing electric fields and Lie algebra transformations to optimize speed and fidelity in quantum operations.

Contribution

It introduces a simplified Hamiltonian transformation for efficient spin manipulation and analyzes the fundamental speed limits under electric field constraints.

Findings

Achieved fast spin control with high fidelity.

Identified lower bounds for operation time based on electric field amplitude.

Demonstrated robustness against noise and systematic errors.

Abstract

The techniques of shortcuts to adiabaticity have been proposed to accelerate the "slow" adiabatic processes in various quantum systems with the applications in quantum information processing. In this paper, we study the counter-diabatic driving for fast adiabatic spin manipulation in a two-electron double quantum dot by designing time-dependent electric fields in the presence of spin-orbit coupling. To simplify implementation and find an alternative shortcut, we further transform the Hamiltonian in term of Lie algebra, which allows one to use a single Cartesian component of electric fields. In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given. Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.