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Quantum states picked from non-trivial symmetry protected topological (SPT)phases have computational power in measurement based quantum computation. Thispower is uniform across SPT phases, and is unlocked by measurements that breakthe symmetry. Except at special points in the phase, all computational schemesknown to date place these symmetry-breaking measurements far apart, to avoidthe correlations introduced by spurious, non-universal entanglement. In thiswork, we investigate the opposite regime of computation where thesymmetry-breaking measurements are packed densely. We show that not only doesthe computation still function, but in fact, under reasonable physicalassumptions, this is the most resource efficient mode.

Counter-intuitive yet efficient regimes for measurement based quantum computation on symmetry protected spin chains