Novel schemes for measurement-based quantum computation

Abstract

We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique further develops tools from many-body physics - based on finitely correlated or projected entangled pair states - to go beyond the cluster-state based one-way computer. We identify resource states that are radically different from the cluster state, in that they exhibit non-vanishing correlation functions, can partly be prepared using gates with non-maximal entangling power, or have very different local entanglement properties. In the computational models, the randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. Finally, we comment on the possibility of tailoring computational models to specific physical systems as, e.g. cold atoms in optical lattices.

5 pages RevTeX, 1 figure, many diagrams. Title changed, presentation improved, material added

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Cited by in corpus (25)

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• Measurement-based quantum computation beyond the one-way model
• Computational power of correlations
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Effective spin systems in coupled micro-cavities
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Percolation, renormalization, and quantum computing with non-deterministic gates
• Fundamentals of universality in one-way quantum computation
• On measurement-based quantum computation with the toric code states
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• The Optical Frequency Comb as a One-Way Quantum Computer
• Phase transition of computational power in the resource states for one-way quantum computation
• Graph states as ground states of many-body spin-1/2 Hamiltonians
• Quantum computation in correlation space and extremal entanglement
• Creation of resilient entangled states and a resource for measurement-based quantum computation with optical superlattices
• Generalized Ardehali-Bell inequalities for graph states
• Thermal robustness of multipartite entanglement of the 1-D spin 1/2 XY model
• Compact Toffoli gate using weighted graph states
• Spin lattices with two-body Hamiltonians for which the ground state encodes a cluster state
• Random circuits by measurements on weighted graph states
• How much of one-way computation is just thermodynamics?
• Characterizing measurement-based quantum gates in quantum many-body systems using correlation functions
• Classical spin systems and the quantum stabilizer formalism: general mappings and applications
• Percolation in quantum computation and communication
• Quantum algorithm for Bose-Einstein condensate quantum fluid dynamics