Quantum robust control theory for Hamiltonian and control field uncertainty*

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