Application of the Small Tip-Angle approximation in the Toggling Frame for the design of analytic robust pulses in Quantum Control

TL;DR

This paper introduces an analytical method using the Small Tip-Angle approximation in the Toggling Frame to design robust quantum control pulses that are resilient to resonance offsets, with practical parameterizations and comparisons to numerical solutions.

Contribution

It presents a novel analytical approach for designing robust quantum control pulses using the Small Tip-Angle approximation, enabling arbitrary order robustness and accommodating experimental constraints.

Findings

Achieves broadband and local robustness up to arbitrary order.

Provides control parameterizations satisfying experimental constraints.

Shows favorable comparison with numerical optimal solutions.

Abstract

We apply the Small Tip-Angle Approximation in the Toggling Frame in order to analytically design robust pulses against resonance offsets for state to state transfer in two-level quantum systems. We show that a broadband or a local robustness up to an arbitrary order can be achieved. We provide different control parameterizations to satisfy experimental constraints and limitations on the amplitude or energy of the pulse. A comparison with numerical optimal solutions is made.