Measurement-based quantum computation in a 2D phase of matter

Abstract

Recently it has been shown that the non-local correlations needed for measurement based quantum computation (MBQC) can be revealed in the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model involving nearest neighbor spin-3/2 interactions on a honeycomb lattice. This state is not singular but resides in the disordered phase of ground states of a large family of Hamiltonians characterized by short-range-correlated valence bond solid states. By applying local filtering and adaptive single particle measurements we show that most states in the disordered phase can be reduced to a graph of correlated qubits that is a scalable resource for MBQC. At the transition between the disordered and Neel ordered phases we find a transition from universal to non-universal states as witnessed by the scaling of percolation in the reduced graph state.

8 pages, 6 figures, comments welcome. v2: published version

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Cited by in corpus (37)

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• Computational Power of Symmetry-Protected Topological Phases
• Verification of Many-Qubit States
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• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Verified measurement-based quantum computing with hypergraph states
• Symmetry-protected topological phases with uniform computational power in one dimension
• Symmetry protection of measurement-based quantum computation in ground states
• Symmetry-protected self-correcting quantum memories
• Qudit quantum computation on matrix product states with global symmetry
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Symmetry-protected topologically ordered states for universal quantum computation
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Quantum spin systems for measurement-based quantum computation
• Hybrid valence-bond states for universal quantum computation
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Quantum information in the Posner model of quantum cognition
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
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• AKLT models on decorated square lattices are gapped
• Measurement-Based Quantum Computing with Valence-Bond-Solids
• Holonomic quantum computing in symmetry-protected ground states of spin chains
• Graph states as ground states of two-body frustration-free Hamiltonians
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Transitions in the quantum computational power
• The Gauge Theory of Measurement-Based Quantum Computation
• Response to defects in multi- and bipartite entanglement of isotropic quantum spin networks
• Spectral properties for a family of two-dimensional quantum antiferromagnets
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• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
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• Interrelations among frustration-free models via Witten's conjugation