Nonperturbative Leakage Elimination Operators and Control of a Three-Level System

TL;DR

This paper analyzes non-ideal leakage elimination operators (LEOs) for three-level quantum systems, demonstrating their effectiveness in reducing errors under realistic experimental conditions through pulse sequence optimization.

Contribution

It introduces a detailed analysis of non-ideal LEO pulses, highlighting their dependence on pulse integral and timing parameters for error suppression in quantum systems.

Findings

LEOs effectively reduce leakage errors with proper pulse parameters

Performance depends on pulse integral and timing ratio

Disordered pulses can still provide error protection

Abstract

Dynamical decoupling operations have been shown to reduce errors in quantum information processing. Leakage from an encoded subspace to the rest of the system space is a particularly serious problem for which leakage elimination operators (LEO) were introduced. These are a particular type of decoupling which are designed to eliminate such leakage errors. Here, we provide an analysis of non-ideal pulses, rather than the well-understood ideal pulses or bang-bang controls. We show that under realistic conditions for experiments these controls will provide protection from errors. Furthermore, we find that the effect of LEOs depends exclusively on the integral of the pulse sequence in the time domain with proper ratio of pulse duration time and its period. When these two key parameters are chosen within certain bounds, leakage errors of the open system (exemplified by a three-level system for the nitrogen-vacancy centers under external magnetic field) would be dramatically decreased. The results are illustrated by the fidelity dynamics of LEO sequences, ranging from regular rectangular pulses, random pulses and even disordered (noisy) pulses.