Optimization of Short Coherent Control Pulses

TL;DR

This paper develops a method to optimize short, finite-duration control pulses for two-level quantum systems, minimizing errors caused by non-commuting system and bath Hamiltonians.

Contribution

It derives correction terms for pulse evolution and provides optimized pulse shapes for specific quantum control operations.

Findings

Optimized pulse shapes for $b1$ and $b1/2$ pulses are presented.

Conditions to eliminate leading-order errors are identified.

The approach improves control fidelity in quantum systems.

Abstract

The coherent control of small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the non-commutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for $\pi$ and $\frac{\pi}{2}$ pulses.