2014/08/16 by Edmond Jonckheere, Frank Langbein, Frank C. Langbein +5
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Neural Networks and Reservoir Computing #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.48550/arxiv.1408.3765
Completely revised and significantly expanded version, accepted for QINP
openalex publication_date 2014/08/16 · arxiv created 2015/10/09 · arxiv updated 2015/10/12 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
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.