For any gate realizable in an ideal model, Theorem 1 bounds the worst-case fidelity from below by a function of only the gate time and an aggregate uncertainty frequency.
Structured singular value analysis for spintronics network information transfer control
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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 $\mu$-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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A Fundamental Bound for Robust Quantum Gate Control
For any gate realizable in an ideal model, Theorem 1 bounds the worst-case fidelity from below by a function of only the gate time and an aggregate uncertainty frequency.