An adiabatic Leakage Elimination Operator in experimental framework

TL;DR

This paper introduces a method to improve quantum adiabatic processes by adding Leakage Elimination Operators (LEO), which are pulse controls that reduce errors and are adaptable to experimental setups.

Contribution

The authors develop an analytical framework for implementing LEO in quantum systems using Feshbach partitioning and counter unitary transformations, enhancing adiabatic process reliability.

Findings

LEO effectiveness depends on control frequency, not pulse shape

Analytical solutions trace the target eigenstate footprint

Control functions are equivalent across formalisms

Abstract

Adiabatic evolution is used in a variety of quantum information processing tasks. However, the elimination of errors is not as well-developed as it is for circuit model processing. Here, we present a strategy to accelerate a reliable quantum adiabatic process by adding Leakage Elimination Operators (LEO) to the evolution which are a sequence of pulse controls acting in an adiabatic subspace. Using the Feshbach $PQ$ partitioning technique, we obtain an analytical solution which traces the footprint of the target eigenstate. The effectiveness of the LEO is independent of the specific form of the pulse but depends on the average frequency of the control function. Furthermore, we give the exact expression of the control function in an experimental framework by a counter unitary transformation, thus the physical meaning of the LEO is clear. Our results reveal the equivalence of the control function between two different formalisms which aids in implementation.