Sensitivity and Robustness of Quantum Spin-1/2 Rings to Parameter Uncertainty

TL;DR

This paper investigates how quantum spin-1/2 rings' transfer fidelity responds to parameter uncertainties, analyzing classical and non-classical sensitivity behaviors to improve robustness in quantum information transfer.

Contribution

It extends previous studies by examining classical and non-classical sensitivity behaviors in an 11-spin ring with specific parameter uncertainties.

Findings

Logarithmic sensitivity can be minimized for certain controllers.

Robustness varies with classical and non-classical behaviors.

Analysis includes effects of coupling strength and bias spillage.

Abstract

Selective transfer of information between spin-1/2 particles arranged in a ring is achieved by optimizing the transfer fidelity over a readout time window via shaping, externally applied, static bias fields. Such static control fields have properties that clash with the expectations of classical control theory. Previous work has shown that there are cases in which the logarithmic differential sensitivity of the transfer fidelity to uncertainty in coupling strength or spillage of the bias field to adjacent spins is minimized by controllers that produce the best fidelity. Here we expand upon these examples and examine cases of both classical and non-classical behavior of logarithmic sensitivity to parameter uncertainty and robustness as measured by the $\mu$ function for quantum systems. In particular we examine these properties in an 11-spin ring with a single uncertainty in coupling strength or a single bias spillage.