# Adiabatic evolution under quantum control

## TL;DR

This paper proposes two novel schemes to accelerate adiabatic quantum evolution, one requiring no prior knowledge of eigenstates and the other utilizing the target eigenstate, demonstrated on a two-level system.

## Contribution

It introduces two new control schemes for speeding up adiabatic evolution, expanding the applicability of adiabatic quantum computation.

## Key findings

- Both schemes successfully accelerate adiabatic evolution in a two-level system.
- The scheme without prior eigenstate knowledge is practical for quantum computation.
- The physics behind the control schemes is thoroughly explained.

## Abstract

One of the difficulties in adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation, we design one of the schemes without any prior knowledge of the instantaneous eigenstates of the final Hamiltonian. Whereas in another scheme, the control is constructed with the instantaneous eigenstate that is the target state of the control. As an illustration, we study a two-level system driven by a time-dependent magnetic field under the control. The physics behind the control scheme is explained.