In my talk I first give an introduction to fault-tolerant quantum computation in the setting of two-dimensional lattices of qubits in which only nearest neighbors may interact. However, decoherence can be counteracted by quantum error-correction. In realistic physical systems, decoherence acts to transform these states into more classical ones, compromising their computational power. Exotic quantum states are created in the process, exhibiting entanglement among large number of particles across macroscopic distances.
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