arXiv subjects

Frank Langbein

Publications and source records attributed to Frank Langbein.

7 recordsLinked to original sources

arXiv2023

Robustness of Energy Landscape Controllers for Spin Rings under Coherent Excitation Transport

The design and analysis of controllers to regulate excitation transport in quantum spin rings presents challenges in the application of classical feedback control techniques to synthesize effective control, and generates results in contradiction to the expectations of classical control theory. In this paper, we examine the robustness of controllers designed to optimize the fidelity of an excitation transfer to uncertainty in system and control parameters. We use the logarithmic sensitivity of the fidelity error as the measure of robustness, drawing on the classical control analog of the sensitivity of the tracking error. In our analysis we demonstrate that quantum systems optimized for coherent transport demonstrate significantly different correlation between error and the log-sensitivity depending on whether the controller is optimized for readout at an exact time T or over a time-window about T.

quant-ph↗

arXiv2017

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

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 $μ$ 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.

quant-ph↗

arXiv2015

Information Transfer Fidelity in Spin Networks and Ring-based Quantum Routers

Spin networks are endowed with an Information Transfer Fidelity (ITF), which defines an absolute upper bound on the probability of transmission of an excitation from one spin to another. The ITF is easily computable but the bound can be reached asymptotically in time only under certain conditions. General conditions for attainability of the bound are established and the process of achiev-ing the maximum transfer probability is given a dynamical model, the translation on the torus. The time to reach the maximum probability is estimated using the simultaneous Diophantine approximation, implemented using a variant of the Lenstra-Lenstra-Lovasz (LLL) algorithm. For a ring with uniform couplings, the network can be made a metric space by defining a distance (satisfying the triangle inequality) that quantifies the lack of transmission fidelity between two nodes. It is shown that transfer fidelities and transfer times can be improved significantly by means of simple controls taking the form of non-dynamic, spatially localized bias fields, opening up the possibility for intelligent design of spin networks and dynamic routing of information encoded in them, while being more flexible than engineering fixed couplings to favor some transfers, and less demanding than control schemes requiring fast dynamic controls.

quant-ph↗

arXiv2015

Time optimal information transfer in spintronics networks

Propagation of information encoded in spin degrees of freedom through networks of coupled spins enables important applications in spintronics and quantum information processing. We study control of information propagation in networks of spin-$\tfrac{1}{2}$ particles with uniform nearest neighbour couplings forming a ring with a single excitation in the network as simple prototype of a router for spin-based information. Specifically optimising spatially distributed potentials, which remain constant during information transfer, simplifies the implementation of the routing scheme. However, the limited degrees of freedom makes finding a control that maximises the transfer probability in a short time difficult. We show that the structure of the eigenvalues and eigenvectors must fulfill a specific condition to be able to maximise the transfer fidelity, and demonstrate that a specific choice among the many potential structures that fulfill this condition significantly improves the solutions found by optimal control.

quant-ph↗

arXiv2014

The ubiquitous problem of learning system parameters for dissipative two-level quantum systems: Fourier analysis versus Bayesian estimation

We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and maximum likelihood estimation is superior to common techniques based on Fourier analysis. Even for simple two-parameter estimation problems, the Bayesian approach yields higher accuracy and precision for the parameter estimates obtained. It requires less data, is more flexible in dealing with different model systems, can deal better with uncertainty in initial conditions and measurements, and enables adaptive refinement of the estimates. The comparison results shows that this holds for measurements of large ensembles of spins and atoms limited by Gaussian noise as well as projection noise limited data from repeated single-shot measurements of a single quantum device.

quant-ph↗

arXiv2014

Curvature of quantum rings

We develop a geometric approach to spin networks with Heisenberg or XX coupling. Geometry is acquired by defining a distance on the discrete set of spins. The key feature of the geometry of such networks is their Gauss curvature $κ$, viewed here as the ability to isometrically embed the chain in the standard Riemannian manifold of curvature $κ$. Here we focus on spin rings. Even though their visual geometry is trivial, it turns out that the geometry they acquire from the quantum mechanical distance is far from trivial.

math-ph↗

arXiv2014

Characterization and Control of Quantum Spin Chains and Rings

Information flow in quantum spin networks is considered. Two types of control -- temporal bang-bang switching control and control by varying spatial degrees of freedom -- are explored and shown to be effective in speeding up information transfer and increasing transfer fidelities. The control is model-based and therefore relies on accurate knowledge of the system parameters. An efficient protocol for simultaneous identification of the coupling strength and the exact number of spins in a chain is presented.

quant-ph↗