Reverse engineering of one-qubit filter functions with dynamical invariants

TL;DR

This paper develops a method to design robust one-qubit control pulses using dynamical invariants, significantly improving gate fidelity and robustness against noise compared to existing techniques.

Contribution

It introduces an integral expression for the filter-transfer function and a cost function for optimizing noise-robust control pulses using dynamical invariant theory.

Findings

Achieved an order of magnitude improvement in gate fidelity.

Designed control pulses that suppress broadband noise effectively.

Proved robustness of nonadiabatic geometric quantum gates under certain errors.

Abstract

We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.