Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we give a detailed account of recent results in which we showed that topological quantum memories can simultaneously tolerate both loss errors and
computational errors, with a graceful tradeoff between the threshold for each. We further discuss a number of subtleties that arise when implementing error correction on topological memories. We particularly focus on the role played by degeneracy in the matching algorithms, and present a systematic study its effects on thresholds. We also discuss some of the implications of degeneracy for estimating phase transition temperatures in the random bond Ising model.
Atomic ensembles, comprising clouds of atoms addressed by laser fields, provide an attractive system for both the storage of quantum information, and the coherent conversion of quantum information between atomic and optical degrees of freedom. In a l
andmark paper, Duan et al. (DLCZ) [1] showed that atomic ensembles could be used as nodes of a quantum repeater network capable of sharing pairwise quantum entanglement between systems separated by arbitrarily large distances. In recent years, a number of promising experiments have demonstrated key aspects of this proposal [2-7]. Here, we describe a scheme for full scale quantum computing with atomic ensembles. Our scheme uses similar methods to those already demonstrated experimentally, and yet has information processing capabilities far beyond those of a quantum repeater.
