Quantum Optimal Control with Geodesic Pulse Engineering

TL;DR

This paper introduces GEOPE, a novel quantum optimal control algorithm that leverages geodesic paths on the unitary manifold to efficiently design multi-qubit quantum gates under experimental constraints, outperforming traditional methods.

Contribution

The paper presents GEOPE, a new geodesic-based control algorithm that improves convergence speed and solution accessibility over existing gradient-based methods like GRAPE.

Findings

GEOPE converges faster than GRAPE for multi-qubit gates.

GEOPE finds solutions inaccessible to GRAPE within reasonable time.

Demonstrated effectiveness on 2D neutral Rydberg atom platforms.

Abstract

Designing multi-qubit quantum logic gates with experimental constraints is an important problem in quantum computing. Here, we develop a new quantum optimal control algorithm for finding unitary transformations with constraints on the Hamiltonian. The algorithm, geodesic pulse engineering (GEOPE), uses differential programming and geodesics on the Riemannian manifold of $\textrm{SU}(2^n)$ for $n$ qubits. We demonstrate significant improvements over the widely used gradient-based method, GRAPE, for designing multi-qubit quantum gates. Instead of a local gradient descent, the parameter updates of GEOPE are designed to follow the geodesic to the target unitary as closely as possible. We present numerical results that show that our algorithm converges significantly faster than GRAPE for a range of gates and can find solutions that are not accessible to GRAPE in a reasonable amount of time. The strength of the method is illustrtated with varied multi-qubit gates in 2D neutral Rydberg atom platforms.