Statistically Characterising Robustness and Fidelity of Quantum Controls and Quantum Control Algorithms

Abstract

Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (RIM${}_p$) is introduced to statistically quantify the robustness and fidelity of a controller as the p-order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The RIM${}_p$ is the p-th root of the p-th raw moment of the infidelity distribution. Using a metrization argument, we justify why RIM${}_1$ (the average infidelity) suffices as a practical robustness measure. Based on the RIM${}_p$, an algorithmic robustness-infidelity measure (ARIM) is developed to quantify the expected robustness and fidelity of controllers found by a control algorithm. The utility of the RIM and ARIM is demonstrated by considering the problem of robust control of spin-$\frac{1}{2}$ networks using energy landscape shaping subject to Hamiltonian uncertainty. The robustness and fidelity of individual control solutions as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and non-stochastic optimization objectives are considered, with the goal of effective RIM optimization in the latter. Although high fidelity and robustness are often conflicting objectives, some high fidelity, robust controllers can usually be found, irrespective of the choice of the quantum control algorithm. However, for noisy optimization objectives, adaptive sequential decision making approaches such as reinforcement learning have a cost advantage compared to standard control algorithms and, in contrast, the infidelities obtained are more consistent with higher RIM values for low noise levels.

13+11 pages, 6+10 figures, revised version, accepted by Phys. Rev. A

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Cited by in corpus (6)

• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls
• Supervised learning for robust quantum control in composite-pulse systems
• Application of the Pontryagin Maximum Principle to the robust time-optimal control of two-level quantum systems
• Analyzing and Unifying Robustness Measures for Excitation Transfer Control in Spin Networks
• Geometric Interpretation of Sensitivity to Structured Uncertainties in Spintronic Networks
• Resilience-Runtime Tradeoff Relations for Quantum Algorithms