Decoherence-based exploration of d-dimensional one-way quantum computation: Information transfer and basic gates

We study the effects of amplitude and phase damping decoherence in d-dimensional one-way quantum computation. We focus our attention on low dimensions and elementary unidimensional cluster state resources. Our investigation shows how information transfer and entangling gate simulations are affected for d >= 2. To understand motivations for extending the one-way model to higher dimensions, we describe how basic qudit cluster states deteriorate under environmental noise of experimental interest. In order to protect quantum information from the environment, we consider encoding logical qubits into qudits and compare entangled pairs of linear qubit-cluster states to single qudit clusters of equal length and total dimension. A significant reduction in the performance of cluster state resources for d > 2 is found when Markovian-type decoherence models are present.