Sensitivity and robustness of quantum spin-1 rings to parameter uncertainty

Intl J Robust & Nonlinear

Langbein

2018

Summary The selective information transfer in spin ring networks by energy landscape shaping control has the property that the error, 1‐prob, where prob is the transfer success probability, and the sensitivity of the error to spin coupling uncertainties are statistically increasing across a family of controllers of increasing error. The need for a statistical hypothesis testing of a concordant trend is made necessary by the noisy behavior of the sensitivity versus the error as a consequence of the optimization of the controllers in a challenging error landscape. Here, we examine the concordant trend between the error and another measure of performance, ie, the logarithmic sensitivity, used in robust control to formulate a well‐known fundamental limitation. Contrary to error versus sensitivity, the error‐versus‐logarithmic‐sensitivity trend is less obvious because of the amplification of the noise due to the logarithmic normalization. This results in the Kendall τ test for rank correlation between the error and the log sensitivity to be somewhat pessimistic with marginal significance level. Here, it is shown that the Jonckheere‐Terpstra test, because it tests the alternative hypothesis of an ordering of the medians of some groups of log sensitivity data, alleviates this statistical problem. This identifies cases of concordant trend between the error and the logarithmic sensitivity, ie, a highly anticlassical feature that goes against the well‐known sensitivity versus the complementary sensitivity limitation.

Section: Methods—type I Errormentioning

confidence: 99%

Section: Conclusion and Future Research Directionsmentioning

confidence: 99%

Section: Conclusion and Future Research Directionsmentioning

confidence: 99%

See 1 more Smart Citation

Jonckheere‐Terpstra test for nonclassical error versus log‐sensitivity relationship of quantum spin network controllers

Jonckheere

Intl J Robust & Nonlinear

Langbein

2018

“…It was shown in previous work [16] that these controllers have interesting robustness properties in that the differential sensitivity of the transfer fidelity for superoptimal controllers, i.e., controllers that achieve unit-fidelity transfer, vanishes, which runs counter to the trade-off between performance and robustness that is commonly seen for classical systems [15]. However, other work indicates that this performance advantage disappears in the presence of decoherence [14], [17]. Moreover, differential sensitivity gives no information how the system responds to larger perturbations over a prolonged period of time, or what the critical frequencies are.…”

Section: Controlled Spin Networkmentioning

confidence: 93%

Robustness of Quantum Systems Subject to Decoherence: Structured Singular Value Analysis?

2021 60th IEEE Conference on Decision and Control (CDC)

Langbein

Weidner

et al. 2021

We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller nor physically relevant structured uncertainties can alter this situation. This changes for open systems where decoherence ensures asymptotic stability and creates a unique landscape of pure performance robustness, with the distinctive feature that closed-loop stability is secured by the underlying physics and needs not be enforced. This stability, however, is often detrimental to quantum-enhanced performance, and additive perturbations of the Hamiltonian give rise to dynamic generators that are nonlinear in the perturbed parameters, invalidating classical paradigms to assess robustness to structured perturbations such as singular value analysis. This problem is addressed using a fixed-point iteration approach to determine a maximum perturbation strength δmax that ensures that the transfer function remains bounded, ||T δ || < δ −1 for δ < δmax.

“…Comparing Eqs. ( 15) and (17), it follows that the steady states for the dephasing system can be related, via ρ ∞ , to the long-term time-averaged states for the fully coherent case.…”

Section: Long-term Time-averages and Asymptotic Steady Statesmentioning

confidence: 96%

Robustness of Energy Landscape Control for Spin Networks Under Decoherence

2018 IEEE Conference on Decision and Control (CDC)

Jonckheere²,

O'Neil

et al. 2018

Quantum spin networks form a generic system to describe a range of quantum devices for quantum information processing and sensing applications. Understanding how to control them is essential to achieve devices with practical functionalities. Energy landscape shaping is a novel control paradigm to achieve selective transfer of excitations in a spin network with surprisingly strong robustness towards uncertainties in the Hamiltonians. Here we study the effect of decoherence, specifically generic pure dephasing, on the robustness of these controllers. Results indicate that while the effectiveness of the controllers is reduced by decoherence, certain controllers remain sufficiently effective, indicating potential to find highly effective controllers without exact knowledge of the decoherence processes.