  Measurement based quantum computation (MBQC), which requires only single
particle measurements on a universal resource state to achieve the full power
of quantum computing, has been recognized as one of the most promising models
for the physical realization of quantum computers. Despite considerable
progress in the last decade, it remains a great challenge to search for new
universal resource states with naturally occurring Hamiltonians, and to better
understand the entanglement structure of these kinds of states. Here we show
that most of the resource states currently known can be reduced to the cluster
state, the first known universal resource state, via adaptive local
measurements at a constant cost. This new quantum state reduction scheme
provides simpler proofs of universality of resource states and opens up plenty
of space to the search of new resource states, including an example based on
the one-parameter deformation of the AKLT state studied in [Commun. Math. Phys.
144, 443 (1992)] by M. Fannes et al. about twenty years ago.
