Quantum Computational Universality of the 2D Cai-Miyake-D\"ur-Briegel Quantum State

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 {\bf 82}, 052309 (2010)]. They showed that this state enables universal quantum computation by constructing single- and two-qubit universal gates. 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 one-dimensional cluster state and entangling gates between two neighboring logical qubits can be implemented by single-spin measurements. Furthermore, a two-dimensional cluster state can be distilled from the Cai-Miyake-D\"ur-Briegel state.