1105.5635 (Tzu-Chieh Wei et al.)

Quantum computational universality of the Cai-Miyake-Dür-Briegel 2D
quantum state from Affleck-Kennedy-Lieb-Tasaki quasichains    [PDF]

Tzu-Chieh Wei, Robert Raussendorf, Leong Chuan Kwek

Universal quantum computation can be achieved by simply performing
single-qubit measurements on a highly entangled resource state, such as cluster
states. Cai, Miyake, D\"ur, and Briegel recently constructed a ground state of
a two-dimensional quantum magnet by combining multiple
Affleck-Kennedy-Lieb-Tasaki quasichains of mixed spin-3/2 and spin-1/2 entities
and by mapping pairs of neighboring spin-1/2 particles to individual spin-3/2
particles [Phys. Rev. A 82, 052309 (2010)]. They showed that this state enables
universal quantum computation by single-spin measurements. Here, we give an
alternative understanding of how this state gives rise to universal
measurement-based quantum computation: by local operations, each quasichain can
be converted to a 1D cluster state and entangling gates between two neighboring
logical qubits can be implemented by single-spin measurements. We further argue
that a 2D cluster state can be distilled from the Cai-Miyake-D\"ur-Briegel
state.

View original: http://arxiv.org/abs/1105.5635