Abstract
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---Lovasz (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.
Highlights
Efficient and controllable transport of information is crucial for information processing, both classical and quantum
The natural coupling among the spins allows the excitation at i to drift toward an excitation at j with an information transfer fidelity (ITF) that can be quantified by the maximum transition probability pmax(i, j)
The previous example illustrates how we can use the weighted LLL-algorithm to find optimal transfer times that yield very high transfer fidelities, and how we can control the margins of error and ensure the parity constraints are satisfied by adjusting the scaling parameter and diagonal weights in the algorithm
Summary
Efficient and controllable transport of information is crucial for information processing, both classical and quantum. While bosonic channels [1] are the most attractive option for long-distance communication, efficient on-chip interconnectivity in a quantum processor based on atomic, ionic or quantum dot-based qubits, or quantum spintronic devices [2], will require direct information transport through networks of coupled solid-state qubits Such networks can be modeled via interacting spins and are generally referred to as spin networks. While it is satisfied for the end nodes of a chain with uniform couplings [13], such chains are usually not considered to admit perfect state transfer except for chains of length two or three This raises the question of the attainability of the upper bound given by the information transfer fidelity. The information transfer infidelity induces a metric that captures how close two nodes in a spin network are from an information-theoretic point of view This information transfer geometry is investigated in Sect.
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