Pulse Quality Optimisation in Quantum Optimal Control

TL;DR

The paper introduces GECKO, a geometric quantum control method that optimizes control pulses post high-fidelity solutions by leveraging the Riemannian geometry of the special unitary group.

Contribution

GECKO is a model-agnostic technique that improves quantum control pulses by navigating level sets in the control landscape for enhanced pulse qualities.

Findings

GECKO improves spectral filtering, smoothness, and robustness of control pulses.

GECKO finds substantially improved pulse solutions across different quantum gates.

The method is demonstrated on a transverse-field Ising model implementing CZ and CNOT gates.

Abstract

Quantum optimal control methods are widely used to design experimental control pulses such as laser amplitudes, phases, or detunings, that implement a target unitary evolution. In practice, what makes a pulse "good" depends not only on its fidelity, but also on the experimental setting and the relevant hardware constraints. Here, we introduce geometric quantum control with kernel optimisation (GECKO), a model-agnostic method for improving control pulses after a high-fidelity solution has been found. GECKO uses the Riemannian geometry of the special unitary group to identify directions in pulse space that leave the implemented unitary unchanged to first order, allowing one to traverse level sets of the control landscape while optimising a chosen differentiable pulse-quality function. We demonstrate GECKO on a transverse-field Ising Hamiltonian implementing CZ and CNOT gates, optimising pulse properties including spectral filtering, smoothness, robustness to parameter deviations, and pulse duration. In all cases, GECKO finds substantially improved pulse solutions.