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

Abstract

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. Cai, Miyake, Dür, 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-Dür-Briegel state.

8 pages, 6 figures, almost published version, journal reference added

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Cited by in corpus (5)

• Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
• Measurement-Based Quantum Computing with Valence-Bond-Solids
• Graph states as ground states of two-body frustration-free Hamiltonians
• Dual quantum-correlation paradigms exhibit opposite statistical-mechanical properties
• Transitions in the quantum computational power