Spatial Control Model and Analysis of Quantum Fields in One-Dimensional Waveguides

Dong, Wenbin; Wu, Rongbo; Zhang, Wei; Li, Chunwen; Tarn, Tzyh-Jong

doi:10.1137/140999190

Cited by 8 publications

(10 citation statements)

References 72 publications

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“…In the definition of quantum control as “tuning quantum interactions between matter and field, or field‐field interaction,” the D ‐controller would fall in the first category as, eg, the electric fields from the gate electrodes control the energy levels of electrons in quantum dots. Here, as in the work of Dong et al, the D ‐controller is taken time‐invariant, but spatially varying. In the aforementioned work, the spatially varying controller is implemented by spatially modifying the dielectric constant of the medium of a wave guide.…”

Section: Excitation Transport In Network Of Spinsmentioning

confidence: 99%

“…Here, as in the work of Dong et al, the D ‐controller is taken time‐invariant, but spatially varying. In the aforementioned work, the spatially varying controller is implemented by spatially modifying the dielectric constant of the medium of a wave guide. This has some commonality with our spatially varying bias field approach; however, our D ‐controller approach seems more related to the DiVincenzo architecture …”

Section: Excitation Transport In Network Of Spinsmentioning

confidence: 99%

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

Jonckheere

Schirmer

Langbein

2018

Intl J Robust & Nonlinear

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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.

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Section: Excitation Transport In Network Of Spinsmentioning

confidence: 99%

Section: Excitation Transport In Network Of Spinsmentioning

confidence: 99%

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

Jonckheere

Schirmer

Langbein

2018

Intl J Robust & Nonlinear

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“…Attempts at classifying the many quantum control laws abound, but here we will particularly retain the classification of [5], which emphasizes, as the present paper does, time-invariant spatially-distributed control. Control is defined in [5] as manipulating matter-field or fieldfield interactions. In this classification, our approach is rather a fieldfield interaction, or in other words our controller is field-mediated.…”

Section: A Information Transfer Controlmentioning

confidence: 97%

“…The same pattern holds for the logarithmic sensitivity, where the expressions in Eqs. (5) are divided by the error, that is, 1 − | OUT|Ψ(t f (m)) | 2 , as shown in Fig. 2.…”

Section: Small Perturbation Sensitivitymentioning

confidence: 99%

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Structured Singular Value Analysis for Spintronics Network Information Transfer Control

Jonckheere

Schirmer²,

Langbein

2017

IEEE Trans. Automat. Contr.

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Control laws for selective transfer of information encoded in excitations of a quantum network, based on shaping the energy landscape using time-invariant, spatially-varying bias fields, can be successfully designed using numerical optimization. Such control laws, already departing from classicality by replacing closed-loop asymptotic stability with alternative notions of localization, have the intriguing property that for all practical purposes they achieve the upper bound on the fidelity, yet the (logarithmic) sensitivity of the fidelity to such structured perturbation as spin coupling errors and bias field leakages is nearly vanishing. Here, these differential sensitivity results are extended to large structured variations using µ-design tools to reveal a crossover region in the space of controllers where objectives usually thought to be conflicting are actually concordant.

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

Weidner,

Reed,

Monroe

et al. 2025

Automatica

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Spatial Control Model and Analysis of Quantum Fields in One-Dimensional Waveguides

Cited by 8 publications

References 72 publications

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

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

Structured Singular Value Analysis for Spintronics Network Information Transfer Control

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

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