Numerical Analysis of Optimized Coherent Control Pulses

TL;DR

This paper numerically analyzes how optimized finite-duration control pulses can effectively approximate ideal instantaneous pulses in qubit systems, highlighting design strategies and limitations.

Contribution

It introduces methods for designing short control pulses that closely mimic ideal pulses, with quantitative analysis of their performance across different coupling regimes.

Findings

Properly designed short pulses can approximate ideal instantaneous pulses.

Discrepancies depend on coupling constants and pulse duration.

Optimized pulses improve control fidelity in quantum systems.

Abstract

Numerically we simulate the effect of optimized coherent control pulses with a finite duration on a qubit in a bath of spins. The pulses of finite duration are compared with ideal instantaneous pulses. In particular, we show that properly designed short pulses can approximate ideal instantaneous pulses up to a certain order in the shortness of the pulse. We provide examples of such pulses, quantify the discrepancy from the ideal case and compare their effect for various ranges of the coupling constants.