Decoherence-based exploration of d-dimensional one-way quantum   computation
  We study the effects of amplitude and phase damping decoherence in d-dimensional one-way quantum computation (QC). 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 d-dimensional qudit cluster states deteriorate under environmental noise. In order to protect quantum information from the environment we consider the encoding of logical qubits into physical qudits and compare entangled pairs of linear qubit-cluster states with single qudit clusters of equal length and total dimension. Our study shows a significant reduction in the performance of one-way QC for d>2 in the presence of Markovian type decoherence models. 
M. S. Tame, M. Paternostro, C. Hadley, S. Bose, M. S. Kim