Structured Singular Value Analysis for Spintronics Network Information Transfer Control

Abstract

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.

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

“…The issue of large as opposed to differential parameter variations is addressed by O'Neil et al and Jonckheere et al, where a structured singular value argument proves that the challenge to the classical limitation remains in force. Note that O'Neil et al not only considered coupling errors but also field focusing errors and that the same μ‐analysis argument() is able to cope with the initial state preparation errors.…”

“…The issue of large as opposed to differential parameter variations is addressed by O'Neil et al and Jonckheere et al, where a structured singular value argument proves that the challenge to the classical limitation remains in force. Note that O'Neil et al not only considered coupling errors but also field focusing errors and that the same μ‐analysis argument() is able to cope with the initial state preparation errors. However, a more challenging robustness problem consists in evaluating the classical limitation in the context of the gap between a model like and some real‐life quantum components like some Copper compounds, which approach the Heisenberg model , but will never quite match the model.…”

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

“…Such systems are interesting from a control theory perspective as they exhibit unusual robustness properties. As demonstrated in [4] and [5], when examining the sensitivity of the system to uncertainty in spin couplings or leakage of the nominal bias field from the intended spin to adjacent spins or measuring the robustness of the system's performance to these same uncertainties we observe trends that appear to contradict the classical control limitations imposed by the identity + = where is the sensitivity transfer matrix and is the complementary sensitivity transfer matrix. To be more precise, we observe cases in which the probability of successful transfer is maximal while the logarithmic sensitivity is nearly zero, in contradiction to the classical intuition [4].…”

“…Additionally, extending the analysis to larger, non-differential uncertainties through -analysis reveals instances of anticlassical behavior with the most optimal controllers also being the most robust in many cases [5]. In this paper, we aim to expand upon the results detailed in [5] by examining a larger data set and looking at cases of both classical as well as anticlassical behavior.…”

Robustness of Energy Landscape Control for Spin Networks Under Decoherence

“…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.…”