Robust quantum control is critical for developing quantum technologies, especially within the noisy intermediatescale quantum (NISQ) era. We introduce the Quantum Control Robustness Landscape (QCRL), a novel framework that maps control parameters to their robustness against noise. This framework offers an efficient mechanism for identifying resilient control solutions. In contrast to the traditional Quantum Control Landscape, which concentrates on optimizing fidelity for specific quantum gates, the QCRL provides a comprehensive perspective on gate engineering by facilitating the navigation of level sets. This capability enables the identification of equally robust control solutions for a universal family of quantum gates, thereby streamlining the process of achieving resilient quantum operations. By exploring these level sets, QCRL serves as a potent tool for both comprehending control schemes and optimizing robust quantum gates with continuous parameters.Robust quantum control is critical for developing quantum technologies, especially within the noisy intermediatescale quantum (NISQ) era. We introduce the Quantum Control Robustness Landscape (QCRL), a novel framework that maps control parameters to their robustness against noise. This framework offers an efficient mechanism for identifying resilient control solutions. In contrast to the traditional Quantum Control Landscape, which concentrates on optimizing fidelity for specific quantum gates, the QCRL provides a comprehensive perspective on gate engineering by facilitating the navigation of level sets. This capability enables the identification of equally robust control solutions for a universal family of quantum gates, thereby streamlining the process of achieving resilient quantum operations. By exploring these level sets, QCRL serves as a potent tool for both comprehending control schemes and optimizing robust quantum gates with continuous parameters.

IEEE International Conference on Quantum Control, Computing and Learning (qCCL)Jun 25, 20250 citations

Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms

Irtaza Khalid, Carrie Ann Weidner, EDMOND A. JONCKHEERE +2 more

Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure ( ${\text{RIM}}_{p}$ ) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the $p\mathrm{th}$ order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The ${\text{RIM}}_{p}$ is the $p\mathrm{th}$ root of the $p\mathrm{th}$ raw moment of the infidelity distribution. Using a metrization argument, we justify why ${\text{RIM}}_{1}$ (the average infidelity) is a good practical robustness measure. Based on the ${\text{RIM}}_{p}$ , 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 on energy landscape controllers of spin- $\frac{1}{2}$ networks subject to Hamiltonian uncertainty. The robustness and fidelity of individual controllers as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and nonstochastic optimization objectives are considered. 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 or stochastic optimization objectives, adaptive sequential decision-making approaches, such as reinforcement learning, have a cost advantage compared to standard control algorithms and, in contrast, the high infidelities obtained are more consistent with high RIM values for low noise levels.Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (${\text{RIM}}_{p}$) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the $p\mathrm{th}$ order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The ${\text{RIM}}_{p}$ is the $p\mathrm{th}$ root of the $p\mathrm{th}$ raw moment of the infidelity distribution. Using a metrization argument, we justify why ${\text{RIM}}_{1}$ (the average infidelity) is a good practical robustness measure. Based on the ${\text{RIM}}_{p}$, 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 on energy landscape controllers of spin-$\frac{1}{2}$ networks subject to Hamiltonian uncertainty. The robustness and fidelity of individual controllers as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and nonstochastic optimization objectives are considered. 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 or stochastic optimization objectives, adaptive sequential decision-making approaches, such as reinforcement learning, have a cost advantage compared to standard control algorithms and, in contrast, the high infidelities obtained are more consistent with high RIM values for low noise levels.

arXiv:2207.07801Physical Review AMar 14, 202314 citations

Advances in Quantum Control Theory

Jeffrey L. Krause

APSMar 1, 20010 citations

Quantum robust control theory for Hamiltonian and control field uncertainty*

Andy Koswara, Vaibhav Bhutoria, Raj Chakrabarti

Abstract Quantum robust control—which can employ fast leading order approximations, slower but more accurate asymptotic methods, or a combination thereof for quantification of robustness—enables control of moments of quantum observables and gates in the presence of Hamiltonian uncertainty or field noise. In this paper, we present a generalized quantum robust control theory that extends the previously described theory of quantum robust control in several important ways. We present robust control theory for control of any moment of arbitrary quantum control objectives, introducing moment-generating functions and transfer functions for quantum robust control that generalize the tools of frequency domain response theory to quantum systems, and extend the Pontryagin maximum principle for quantum control to control optimization in the presence of noise in the manipulated amplitudes or phases used to shape the control field. To provide guidelines as to the types of quantum control systems and control objectives for which asymptotic robustness analysis is important for accuracy, we introduce methods for assessing the Lie algebraic depth of quantum control systems, and illustrate through examples drawn from quantum information processing how such accurate methods for quantification of robustness to noise and uncertainty are more important for control strategies that exploit higher order quantum pathways. In addition, we define the relationship between leading order Taylor expansions and asymptotic estimates for quantum control moments in the presence of Hamiltonian uncertainty and field noise, and apply such leading order approximations to significant pathways analysis and dimensionality reduction of asymptotic quantum robust control calculations, describing numerical methods for implementation of these calculations.Abstract Quantum robust control—which can employ fast leading order approximations, slower but more accurate asymptotic methods, or a combination thereof for quantification of robustness—enables control of moments of quantum observables and gates in the presence of Hamiltonian uncertainty or field noise. In this paper, we present a generalized quantum robust control theory that extends the previously described theory of quantum robust control in several important ways. We present robust control theory for control of any moment of arbitrary quantum control objectives, introducing moment-generating functions and transfer functions for quantum robust control that generalize the tools of frequency domain response theory to quantum systems, and extend the Pontryagin maximum principle for quantum control to control optimization in the presence of noise in the manipulated amplitudes or phases used to shape the control field. To provide guidelines as to the types of quantum control systems and control objectives for which asymptotic robustness analysis is important for accuracy, we introduce methods for assessing the Lie algebraic depth of quantum control systems, and illustrate through examples drawn from quantum information processing how such accurate methods for quantification of robustness to noise and uncertainty are more important for control strategies that exploit higher order quantum pathways. In addition, we define the relationship between leading order Taylor expansions and asymptotic estimates for quantum control moments in the presence of Hamiltonian uncertainty and field noise, and apply such leading order approximations to significant pathways analysis and dimensionality reduction of asymptotic quantum robust control calculations, describing numerical methods for implementation of these calculations.

New Journal of PhysicsMay 24, 202124 citations

Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (

{\text{RIM}}_{p}

) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the

p\mathrm{th}

order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The

{\text{RIM}}_{p}

is the

p\mathrm{th}

root of the

p\mathrm{th}

raw moment of the infidelity distribution. Using a metrization argument, we justify why

{\text{RIM}}_{1}

(the average infidelity) is a good practical robustness measure. Based on the

{\text{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 on energy landscape controllers of spin-

\frac{1}{2}

networks subject to Hamiltonian uncertainty. The robustness and fidelity of individual controllers as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and nonstochastic optimization objectives are considered. 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 or stochastic optimization objectives, adaptive sequential decision-making approaches, such as reinforcement learning, have a cost advantage compared to standard control algorithms and, in contrast, the high infidelities obtained are more consistent with high RIM values for low noise levels.