Time optimal information transfer in spintronics networks

Abstract

Abstract-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. I. INTRODUCTIONEncoding information spin degrees of freedom has the potential to revolutionize information technology via the development of novel spintronic devices and possible future quantum information processors [1], [2]. Utilizing information encoded in spin degrees of freedom, however, requires efficient, controlled on-chip transfer of spin-based information. In some types of spintronic devices, spin degrees of freedom are used in addition to motional degrees of freedom of electrons, and information encoded in the spin degrees of freedom can be transferred using conventional currents. In principle, however, information stored in spin states can propagate through a network of coupled spins without charge transport. As propagation of spin-based information is governed by quantum-mechanics and the Schrödinger equation, however, excitations in a spin network propagate, disperse and refocus in a wave-like manner, and controlling information transport is thus a quantum control problem. Without any means to control the propagation of spin-based information in such networks information transport can be slow and inefficient. Control can be utilized to optimize transport in terms of maximizing transfer efficiency and speed [3], [4]. Here, we consider how to control information propagation in a network of spins by optimizing spatially distributed potentials, which remain constant during the evolution, in contrast to dynamic control schemes, which require dynamic modulation or fast switching of the control potentials.

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

“…The study, therefore, amounts to a total of 108 case studies, where a case study is defined by a number of spins M and an |OUT⟩ spin. For every M ∈[2,3,…,19,20] and every (|IN⟩=1,|OUT⟩≤⌈ M /2⌉) pair, controllers D were computed by numerical optimization runs of relative to D , t f , either at the precise time t f or over a window around t f , and controllers were ordered by the increasing error, as explained in the works of Langbein et al and Schirmer et al) and as illustrated in Figure . Given a case study ( M ,|OUT⟩) out of a total number of 108 case studies, the number N of time‐windowed optimization runs, or controllers, were between 114 and 1998, with an average of 939 controllers.…”

“…Although the basic concepts developed here remain valid for the whole class of such controllers, here, we will more specifically consider controllers that induce energy level shifts. () More specifically, in this paper, D =diag ( D 1 , D 2 ,…, D M ) is a diagonal matrix of bias fields added to the Hamiltonian in some subspace. The concept is illustrated in Figure .…”

“…The problem is that there is no closed‐form solution of the optimization . As shown in Figure 2 in the work of Langbein et al, the error landscape is extremely challenging, and some optimization runs are successful at finding solutions very close to the upper bound, while the other solutions remain trapped in local minima with poor fidelity. The reward of having a variety of controllers achieving various levels of performance from optimal to poor is that it allows us to check, even quantify, the concordance or discordance between the achievable transfer performance and the log sensitivity to the uncertain coupling parameters.…”

Multi-fractal geometry of finite networks of spins: Nonequilibrium dynamics beyond thermalization and many-body-localization

“…In this context one of the most important questions is the capacity of a spin(tronic) network for information transport or teleportation of quantum states between nodes in the network. One measure introduced to capture the intrinsic ability of a quantum network to transport information between nodes through the propagation of excitations is Information Transfer Fidelity (ITF) [16][17][18][19]22]. Broadly, it is an easily computable upper bound on the maximum achievable probability with which an excitation can be successfully propagated from one node to another in the network.…”

“…Rings on the other hand are biased to "quench" the ring to a chain hence favoring transfer near the biased spin [19,22]. In particular, we contrast original and engineered spin chains and original and biased spin rings.…”