On measurement-based quantum computation with the toric code states

Abstract

We study measurement-based quantum computation (MQC) using as quantum resource the planar code state on a two-dimensional square lattice (planar analogue of the toric code). It is shown that MQC with the planar code state can be efficiently simulated on a classical computer if at each step of MQC the sets of measured and unmeasured qubits correspond to connected subsets of the lattice.

9 pages, 5 figures

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• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Novel schemes for measurement-based quantum computation
• Ground state entanglement and geometric entropy in the Kitaev's model
• Universal resources for measurement-based quantum computation
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• Statistical Mechanical Models and Topological Color Codes
• Measurement-based quantum computation and undecidable logic
• A BQP-complete problem related to the Ising model partition function via a new connection between quantum circuits and graphs
• Classical spin systems and the quantum stabilizer formalism: general mappings and applications
• Percolation in quantum computation and communication