Robust Control Performance for Open Quantum Systems

Schirmer, Sophie G.; Langbein, Frank C.; Weidner, Carrie A.; Jonckheere, Edmond

doi:10.48550/arxiv.2008.13691

Cited by 4 publications

(8 citation statements)

References 20 publications

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“…This approach becomes relevant when confidence in an analytical physical model is low or there are missing terms that cannot be analytically or perturbatively accounted for, e.g., complicated noise sources. This is also in accordance with modern robustness theory and the µ function in classical [44] and quantum [45][46][47] settings.…”

Section: Perturbationssupporting

confidence: 90%

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

Khalid¹,

Weidner²,

Jonckheere³

et al. 2022

Preprint

Self Cite

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Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (RIMp) 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 RIMp is the p-th root of the p-th raw moment of the infidelity distribution. Using a metrization argument, we justify why RIM1 (the average infidelity) suffices as a practical robustness measure. Based on the RIMp, 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-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.

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Section: Perturbationssupporting

confidence: 90%

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

Khalid¹,

Weidner²,

Jonckheere³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Robustness against specified frequency bands of the noise power spectral density can be achieved based by including a filter function which can either be derived from reverse engineering [145] or parametrized and optimized [631]. The design of robust control protocols has been explored for different sources of imperfections [49,363,473,507,545] and the optimal control of an inhomogeneous spin ensemble coupled to a cavity has been studied [29].…”

Section: Numerical Approachmentioning

confidence: 99%

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Koch,

Boscain,

Calarco

et al. 2022

Preprint

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Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments.

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“…from the unperturbed or nominal dynamics r to the error dynamics z = r δ − r via the perturbed dynamics r δ as introduced in [9], where S k is a structured perturbation of strength δ and s is the Laplace variable. The Bloch matrix and its structured perturbation take the form…”

Section: B Structured Perturbation Of the Error Transfer Matrixmentioning

confidence: 99%

“…is the matrix #-inverse of (sI − A) developed for such open quantum systems in Ref. [9], with I the 15 × 15 identity matrix. It is then readily verified that z(s) = T z,r (δ, s) r(s) with…”

Section: B Structured Perturbation Of the Error Transfer Matrixmentioning

confidence: 99%

See 1 more Smart Citation

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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Robust Control Performance for Open Quantum Systems

Cited by 4 publications

References 20 publications

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

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

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

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

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