# Optimal superadiabatic population transfer and gates by dynamical phase corrections

## TL;DR

This paper develops a method for fast, high-fidelity quantum state transfer and gate operations using superadiabatic techniques, including counterdiabatic driving and phase corrections, applicable to three-level systems like transmons.

## Contribution

It introduces a way to construct counterdiabatic Hamiltonians for systems with forbidden transitions and corrects for ac-Stark shifts, enabling robust, rapid quantum operations.

## Key findings

- Achieved unit fidelity population transfer with superadiabatic methods.
- Demonstrated a robust superadiabatic NOT-gate in a three-level system.
- Applicable to transmon qubits with ladder energy structures.

## Abstract

In many quantum technologies adiabatic processes are used for coherent quantum state operations, offering inherent robustness to errors in the control parameters. The main limitation is the long operation time resulting from the requirement of adiabaticity. The superadiabatic method allows for faster operation, by applying counterdiabatic driving that corrects for excitations resulting from the violation of the adiabatic condition. In this article we show how to construct the counterdiabatic Hamiltonian in a system with forbidden transitions by using two-photon processes and how to correct for the resulting time-dependent ac-Stark shifts in order to enable population transfer with unit fidelity. We further demonstrate that superadiabatic stimulated Raman passage can realize a robust unitary NOT-gate between the ground state and the second excited state of a three-level system. The results can be readily applied to a three-level transmon with the ladder energy level structure.