Abstract Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates nonlinear dynamics with linear operators. In comparison with many machine learning paradigms minimal data is needed to construct a biDMD model, and the model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.Abstract Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates nonlinear dynamics with linear operators. In comparison with many machine learning paradigms minimal data is needed to construct a biDMD model, and the model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.

arXiv:2010.14577New Journal of PhysicsFeb 24, 202133 citations

Global controllability with a single local actuator

S. G. Schirmer, I. C. H. Pullen, Peter J. Pemberton-Ross

We show that we can achieve global density-operator controllability for most $N$ -dimensional bilinear Hamiltonian control systems with general fixed couplings using a single, locally acting actuator that modulates one energy-level transition. Controllability depends upon the position of the actuator and relies on the absence of either decompositions into noninteracting subgroups or symmetries restricting the dynamics to a subgroup of $\mathrm{SU}(N)$ . These results are applied to spin-chain systems and used to explicitly construct control sequences for a single binary-valued switch actuator.We show that we can achieve global density-operator controllability for most $N$-dimensional bilinear Hamiltonian control systems with general fixed couplings using a single, locally acting actuator that modulates one energy-level transition. Controllability depends upon the position of the actuator and relies on the absence of either decompositions into noninteracting subgroups or symmetries restricting the dynamics to a subgroup of $\mathrm{SU}(N)$. These results are applied to spin-chain systems and used to explicitly construct control sequences for a single binary-valued switch actuator.

arXiv:0801.0721Physical Review ADec 31, 200836 citations

Algebraic dynamics and time-dependent dynamical symmetry of nonautonomous systems

Shun-Jin Wang, Fengyi Li, A. Weiguny

Physics Letters ASep 1, 199368 citations

Classical Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

William M. Watkins, Gregory Quiroz

In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. In this Letter, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while nonsymmetric noise leads to highly specific leakage errors that are block diagonal in the symmetry representation. We support our findings with numerical studies of a transverse-field Ising model and a quantum error detecting code subject to spatiotemporally correlated multiaxis noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. In this Letter, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while nonsymmetric noise leads to highly specific leakage errors that are block diagonal in the symmetry representation. We support our findings with numerical studies of a transverse-field Ising model and a quantum error detecting code subject to spatiotemporally correlated multiaxis noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.

arXiv:2501.06619Physical Review LettersAug 11, 20250 citations

Symmetries in Discrete-Time Mechanics

Mohammad Khorrami

Annals of PhysicsDec 1, 19960 citations

We show that we can achieve global density-operator controllability for most

N

-dimensional bilinear Hamiltonian control systems with general fixed couplings using a single, locally acting actuator that modulates one energy-level transition. Controllability depends upon the position of the actuator and relies on the absence of either decompositions into noninteracting subgroups or symmetries restricting the dynamics to a subgroup of

\mathrm{SU}(N)

. These results are applied to spin-chain systems and used to explicitly construct control sequences for a single binary-valued switch actuator.