An arbitrarily reliable quantum computer can be efficiently constructed fromnoisy components using a recursive simulation procedure, provided that thosecomponents fail with probability less than the fault-tolerance threshold.Recent estimates of the threshold are near some experimentally achieved gatefidelities. However, the landscape of threshold estimates includespseudothresholds, threshold estimates based on a subset of components and a lowlevel of recursion. In this paper, we observe that pseudothresholds are ageneric phenomenon in fault-tolerant computation. We define pseudothresholdsand present classical and quantum fault-tolerant circuits exhibitingpseudothresholds that differ by a factor of 4 from fault-tolerance thresholdsfor typical relationships between component failure rates. We develop tools forvisualizing how reliability is influenced by recursive simulation in order todetermine the asymptotic threshold. Finally, we conjecture that refinements ofthese methods may establish upper bounds on the fault-tolerance threshold forparticular codes and noise models.
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