  While the circuit model of quantum computation defines its logical depth or
"computational time" in terms of temporal gate sequences, the measurement-based
model could allow totally different temporal ordering and parallelization of
logical gates. By developing techniques to analyze Pauli measurements on
multi-qubit hypergraph states generated by the Controlled-Controlled-Z (CCZ)
gates, we introduce a deterministic scheme of universal measurement-based
computation. In contrast to the cluster-state scheme, where the Clifford gates
are parallelizable, our scheme enjoys massive parallelization of CCZ and SWAP
gates, so that the computational depth grows with the number of global
applications of Hadamard gates, or, in other words, with the number of changing
computational bases. A logarithmic-depth implementation of an N-times
Controlled-Z gate illustrates a novel trade-off between space and time
complexity.
