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We examine cluster states transformed by stochastic local operations andclassical communication, as a resource for deterministic universal computationdriven strictly by projective measurements. We identify circumstances underwhich such states in one dimension constitute resources for random lengthsingle-qubit rotations, in one case quasi-deterministically (N-U-N states) andin another probabilistically (B-U-B states). In contrast to the cluster states,the N-U-N states exhibit spin correlation functions that decay exponentiallywith distance, while the B-U-B states can be arbitrarily locally pure. Atwo-dimensional square N-U-N lattice is a universal resource forquasideterministic measurement-based quantum computation. Measurements on cubicB-U-B states yield two-dimensional cluster states with bond defects, whoseconnectivity exceeds the percolation threshold for a critical value of thelocal purity.

Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication