Quantum state reduction for universal measurement based computation

Abstract

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.

5 pages

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Cited by in corpus (22)

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• The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
• Thermal States as Universal Resources for Quantum Computation with Always-on Interactions
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Qudit quantum computation on matrix product states with global symmetry
• No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems
• Measurement-Based Quantum Computation
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Hybrid valence-bond states for universal quantum computation
• Quantum spin systems for measurement-based quantum computation
• Measurement-Based Quantum Computing with Valence-Bond-Solids
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Quantum computational tensor network on string-net condensate
• Quantum computational universality of the Cai-Miyake-Dür-Briegel 2D quantum state from Affleck-Kennedy-Lieb-Tasaki quasichains
• Symmetry constraints on temporal order in measurement-based quantum computation
• Quantum computation by teleportation and symmetry
• Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication
• Topos logic in measurement-based quantum computation