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Energy landscape controllers for quantum state transfer in spin-1/2 networks with ring topology

Frank C. Langbein, Sean P. O’Neil, Sophie Shermer

Published Dec 2, 2022• 12 citations
Publisher

Abstract

This data set contains energy landscape controllers for information propagation in networks of spin-1/2 particles (qubits) with a ring topology and uniform nearest neighbor couplings of XXZ type. The controllers are optimized to maximize the fidelity of excitation transfer between nodes of ring in the single excitation subspace. The network can be regarded as simple prototype of a router for spin-based information. The dataset contains controllers for rings ranging in size from 3 to 20 spins with excitation transfer from node 1 to nodes 2, 3, ... ceil(N/2) considered. Controllers optimized for both instantaneous readout and time-windowed (finite bandwidth) readout are included.

DOI
10.33774/coe-2022-35xgg

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This data set contains energy landscape controllers for information propagation in networks of spin-1/2 particles (qubits) with a ring topology and uniform nearest neighbor couplings of XXZ type. The controllers are optimized to maximize the fidelity of excitation transfer between nodes of ring in the single excitation subspace. The network can be regarded as simple prototype of a router for spin-based information. The dataset contains controllers for rings ranging in size from 3 to 20 spins with excitation transfer from node 1 to nodes 2, 3, ... ceil(N/2) considered. Controllers optimized for both instantaneous readout and time-windowed (finite bandwidth) readout are included.
This data set contains energy landscape controllers for information propagation in networks of spin-1/2 particles (qubits) with a ring topology and uniform nearest neighbor couplings of XXZ type. The controllers are optimized to maximize the fidelity of excitation transfer between nodes of ring in the single excitation subspace. The network can be regarded as simple prototype of a router for spin-based information. The dataset contains controllers for rings ranging in size from 3 to 20 spins with excitation transfer from node 1 to nodes 2, 3, ... ceil(N/2) considered. Controllers optimized for both instantaneous readout and time-windowed (finite bandwidth) readout are included.
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-1/2 particles with uniform nearest neighbor couplings forming a ring with a single excitation in the network as simple prototype of a router for spin-based information. Specifically optimizing 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 maximizes 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 maximize 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.
Information encoded in networks of stationary, interacting spin-1/2 particles is central for many applications ranging from quantum spintronics to quantum information processing. Without control, however, information transfer through such networks is generally inefficient. Currently available control methods to maximize the transfer fidelities and speeds mainly rely on dynamic control using time-varying fields and often assume instantaneous readout. We present an alternative approach to achieving efficient, high-fidelity transfer of excitations by shaping the energy landscape via the design of time-invariant feedback control laws without recourse to dynamic control. Both instantaneous readout and the more realistic case of finite readout windows are considered. The technique can also be used to freeze information by designing energy landscapes that achieve Anderson localization. Perfect state or superoptimal transfer and localization are enabled by conditions on the eigenstructure of the system and signature properties for the eigenvectors. Given the eigenstructure enabled by superoptimality, it is shown that feedback controllers that achieve perfect state transfer are, surprisingly, also the most robust with regard to uncertainties in the system and control parameters.
Abstract 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. This paper examines 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 robustness measure, drawing on the classical control analog of the sensitivity of the tracking error. Our analysis shows 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 T ± Δ /2.
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 achieving 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–Lovász (LLL) algorithm. For a ring with uniform couplings, the network can be made into 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 nondynamic, 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.