Robustness of optimal quantum annealing protocols

TL;DR

This paper studies the robustness of optimal quantum annealing protocols against coherent control errors, showing that robust protocols admit larger smooth annealing sections, which suggests that QA admits improved robustness in comparison to bang-bang solutions such as the quantum approximate optimization algorithm.

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.

Figures (6)

• Figure 1: Example: 8-qubit; $\zeta = 0$; nominal case, i.e., classical QA as in Section \ref{['prb:optimalcontrol']}. This Figure shows the optimal annealing protocol and the conditions for a singular control section. In addition, the corresponding control Hamiltonian $\mathfrak{H}$ is plotted.
• Figure 2: Example: 8-qubit; $\zeta = 0.1$; spectral norm regularization, i.e., $q(u) = \left\| H(u) \right\|_2$. This Figure shows the robust optimal annealing protocol and the conditions for a singular control section. In addition, the corresponding control Hamiltonian $\mathfrak{H}$ is plotted.
• Figure 3: Example: 8-qubit; $\zeta = 0.1$; Frobenius norm as regularization, i.e., $q(u) = \left\| H(u) \right\|_F$. This Figure shows the robust optimal annealing protocol and the conditions for a singular control section. In addition, the corresponding control Hamiltonian $\mathfrak{H}$ is plotted.
• Figure 4: Example: 8-qubit. Worst fidelity the optimal annealing protocols over $\hat{\epsilon}$ corresponding to the four approach nominal, QAOA, spectral norm, Frobenius norm. The worst fidelity describes the worst fidelity in the set of generated error signals scaled according to $\hat{\epsilon}$.
• Figure 5: Example: 8-qubit. Mean objective function value, i.e., equation \ref{['eqs:objectivefunction']}. We are using the set of generated error signals to compute a mean value of $\braket{x_\epsilon(T)|C|x_\epsilon(T)}$.

Theorems & Definitions (4)

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