Robustness of optimal quantum annealing protocols

TL;DR

This paper investigates how to enhance the robustness of quantum annealing protocols against control errors by introducing regularization and analyzing optimality conditions, supported by numerical simulations.

Contribution

It introduces a regularization approach to improve robustness of quantum annealing protocols and analyzes their optimality conditions, highlighting advantages over bang-bang solutions.

Findings

Robust protocols have larger smooth annealing sections.

Hamiltonian norm quantifies robustness against control errors.

Numerical simulations confirm improved robustness of the proposed methods.

Abstract

Noise in quantum computing devices poses a key challenge in their realization. In this paper, we study the robustness of optimal quantum annealing protocols against coherent control errors, which are multiplicative Hamlitonian errors causing detrimental effects on current quantum devices. We show that the norm of the Hamiltonian quantifies the robustness against these errors, motivating the introduction of an additional regularization term in the cost function. We analyze the optimality conditions of the resulting robust quantum optimal control problem based on Pontryagin's maximum principle, showing that robust protocols admit larger smooth annealing sections. This suggests that quantum annealing admits improved robustness in comparison to bang-bang solutions such as the quantum approximate optimization algorithm. Finally, we perform numerical simulations to verify our analytical results and demonstrate the improved robustness of the proposed approach.