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QI: Fachverband Quanteninformation

QI 8: Quantum Computing Theory I

QI 8.4: Vortrag

Montag, 10. März 2025, 18:00–18:15, HS IV

Robustness of optimal quantum annealing protocols — Niklas Funcke and •Julian Berberich — Institute for Systems Theory and Automatic Control, University of Stuttgart, 70569 Stuttgart, Germany

Quantum annealing addresses optimization problems by smoothly interpolating between two Hamiltonians. When implementing quantum annealing protocols on current hardware, errors can cause significant problems and may destroy any potential computational advantages. In this contribution, we study the robustness of optimal quantum annealing protocols against coherent control errors, which correspond to over- or underrotation errors and were shown to be particularly detrimental. We prove that the influence of coherent control errors on quantum annealing is bounded by the norm of the Hamiltonian that is applied to the system. We then leverage this bound to design robust quantum annealing protocols which minimize not only the cost Hamiltonian but also an additional regularization term penalizing the norm of the Hamiltonian. The regularization is weighted by a tuning parameter which allows to trade off two objectives: optimality and robustness. Next, using tools from optimal control theory, we analyze the optimal structure of robust quantum annealing protocols. We prove that the regularization causes a fundamental change of the structure, leading to a higher preference of smooth annealing phases over bang-bang solutions. This provides theoretical evidence that quantum annealing is more robust than variational quantum optimization techniques. Numerical simulations confirm our theoretical findings.

Keywords: Quantum computation; Quantum annealing; Optimal control; Quantum errors; Robustness