P. Aliferis, D. Gottesman, and J. Preskill, "Quantum accuracy threshold for concatenated distance-3 codes," Quant. Inf. Comput. 6 (2006) 97-165, eprint quant-ph/0504218. Gives a new proof of the quantum threshold theorem that applies to codes of distance 3 or greater, and to highly-adversarial stochastic or non-Markovian noise. We also set a lower bound on the quantum threshold of the order of 10^{-5}.
P. Aliferis, and D. P. DiVincenzo, "Effective fault-tolerant quantum computation with slow measurements," Phys. Rev. Lett. 98 (2007) 220501, eprint quant-ph/0607047. We show that the threshold for quantum computation is not significantly affected when measurement times are much longer than gates times. This is particularly important for solid-state quantum computing implementations where measurements can be 1,000 times or more slower than gates.
P. Aliferis, and J. Preskill, "Fault-tolerant quantum computation against biased noise," Quantum Physics (2007), eprint arXiv:0710.1301. We formulate a scheme of fault-tolerant quantum computation that works effectively when noise is highly biased, i.e., when phase errors in the computational basis are much more likely than bit-flip errors.
P. Aliferis, "Threshold lower bounds for Knill's Fibonacci scheme," Quantum Physics (2007), epring arXiv:0709.3603. We give a rigorous analysis of schemes of fault-tolerant quantum computation which are based on message-passing decoding. By analyzing the simplest such scheme, we find a threshold lower bound of the order of 10^{-3} which is the best that has been rigorously established so far.
P. Aliferis, and D. Leung, "Computation by measurements: a unifying picture," Phys. Rev. A 70, 062314 (2004), eprint quant-ph/0404082. We show that all schemes of quantum computation that are based on measurements can be understood as a sequence of gate-teleportation steps.