Dynamical Uncertainty Propagation with Noisy Quantum Parameters

Dalgaard, Mogens; Weidner, Carrie A.; Motzoi, Felix

doi:10.1103/physrevlett.128.150503

Cited by 6 publications

(1 citation statement)

References 60 publications

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“…Robustness for quantum systems is therefore typically assessed via Monte-Carlo simulations, wherein one samples the parameter space of uncertainties and determines averages and distributions of relevant performance measures [7], although there exist other methods for determining uncertainty [8]. Monte-Carlo approaches have their merits, but they are often computationally expensive and rely solely on numerical and statistical analyses.…”

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confidence: 99%

Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations

Weidner¹,

Schirmer²,

Langbein³

et al. 2022

Preprint

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Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfied for closed quantum systems, can be satisfied for open quantum systems where Lindbladian behavior leads to nonunitary evolution, and allows for nonzero classical stability margins, but it remains difficult to extract physical insight when classical robust control tools are applied to these systems. We consider a straightforward example of the entanglement between two qubits dissipatively coupled to a lossy cavity and analyze it using the classical stability margin and structured perturbations. We attempt, where possible, to extract physical insight from these analyses. Our aim is to highlight where classical robust control can assist in the analysis of quantum systems and identify areas where more work needs to be done to develop specific methods for quantum robust control. I. INTRODUCTIONDespite the extensive success and ongoing development of robust control theory [1], the tools developed were found not to be readily applicable to classical systems [2], and they are even less readily adaptable to quantum mechanical systems. This is increasingly problematic amidst the second quantum revolution, when quantum mechanical devices for computing, networking, sensing, and simulation are moving out of laboratories and into commercial markets [3], where robust control of these devices is critical to their utility in real-world settings [4]. These issues arise because quantum systems can be difficult to cast as linear, time-invariant control systems subject to feedback control stabilization. Rather, quantum control systems, especially those that evolve unitarily in so-called closed systems, are typically open-loop bilinear systems, although several types of feedback control for closed-loop quantum systems, using both measurementbased and coherent feedback, have been developed [4], [5].Uncertainties in quantum systems can take the form of structured perturbations in state parameters (similar to classical structured uncertainties), but these uncertainties must arise in such a way that the evolution of the system remains physical and follows the law of quantum mechanics (i.e.

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mentioning

confidence: 99%

Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations

Weidner¹,

Schirmer²,

Langbein³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

Robust quantum control in closed and open systems: Theory and practice

Weidner,

Reed,

Monroe

et al. 2025

Automatica

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Exponentiation of parametric Hamiltonians via unitary interpolation

Schilling,

Preti,

Müller

et al. 2024

Phys. Rev. Research

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The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit compilation, or Monte Carlo sampling. We introduce two ideas for the time-efficient approximation of matrix exponentials of linear multiparametric Hamiltonians. We modify the Suzuki-Trotter product formula from an approximation to an interpolation scheme to improve both accuracy and walltime. This allows us to achieve high fidelities within a single interpolation step, which can be computed directly from cached matrices. Furthermore, we define the interpolation on a grid of system parameters, and show that the interpolation infidelity converges with fourth-order accuracy in the number of interpolation bins. Published by the American Physical Society 2024

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Dynamical Uncertainty Propagation with Noisy Quantum Parameters

Cited by 6 publications

References 60 publications

Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations

Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations

Robust quantum control in closed and open systems: Theory and practice

Exponentiation of parametric Hamiltonians via unitary interpolation

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