# Energetic cost of quantum control protocols

## TL;DR

This paper evaluates the energetic costs of various quantum control protocols, revealing a hierarchy of costs dependent on protocol duration and demonstrating optimization possibilities for cost reduction.

## Contribution

It introduces a quantitative cost measure for quantum control protocols and analyzes their energetic efficiency across multiple models, highlighting potential for cost optimization.

## Key findings

- Hierarchy of control costs based on protocol duration
- Counterdiabatic driving can be optimized to reduce energy expenditure
- Similar cost behaviors observed across different quantum models

## Abstract

We quantitatively assess the energetic cost of several well-known control protocols that achieve a finite time adiabatic dynamics, namely counterdiabatic and local counterdiabatic driving, optimal control, and inverse engineering. By employing a cost measure based on the norm of the total driving Hamiltonian, we show that a hierarchy of costs emerges that is dependent on the protocol duration. As case studies we explore the Landau-Zener model, the quantum harmonic oscillator, and the Jaynes-Cummings model and establish that qualitatively similar results hold in all cases. For the analytically tractable Landau-Zener case, we further relate the effectiveness of a control protocol with the spectral features of the new driving Hamiltonians and show that in the case of counterdiabatic driving, it is possible to further minimize the cost by optimizing the ramp.