# Generalized Shortcuts to Adiabaticity and Enhanced Robustness Against Decoherence

## TL;DR

This paper explores how generalized shortcuts to adiabaticity can be used to achieve faster quantum evolutions with minimal energy, and demonstrates their increased robustness against decoherence in quantum systems.

## Contribution

It introduces a minimal energy scheme for speeding up adiabatic processes and shows how to construct infinite classes of transitionless models, including time-independent Hamiltonians.

## Key findings

- Generalized transitionless evolutions are more robust against decoherence.
- Application to Landau-Zener model shows improved decoherence resistance.
- Quantum gate Hamiltonians also benefit from enhanced robustness.

## Abstract

Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counter-diabatic evolutions, higher speed comes at higher energy cost. Here, the counter-diabatic theory is employed as a minimal energy demanding scheme for speeding up adiabatic tasks. As a by-product, we show that this approach can be used to obtain infinite classes of transitionless models, including time-independent Hamiltonians under certain conditions over the eigenstates of the original Hamiltonian. We apply these results to investigate shortcuts to adiabaticity in decohering environments by introducing the requirement of a fixed energy resource. In this scenario, we show that generalized transitionless evolutions can be more robust against decoherence than their adiabatic counterparts. We illustrate this enhanced robustness both for the Landau-Zener model and for quantum gate Hamiltonians.