Fault-tolerant quantum computation with graph states
Panos Aliferis, Debbie Leung · arXiv (Cornell University) · 2005
The standard quantum accuracy threshold theorem states that if storage errors and gate imperfections at the physical level are sufficiently improbable, local and Markovian, then quantum computation of arbitrary accuracy and scale can be efficiently implemented by concatenated encoding. However, this theorem does not apply straightforwardly to the alternative model of quantum computation using measurements on graph states. This is mainly because, when simulating any quantum circuit within this model, a single physical error can propagate forward and induce multiple correlated errors making the effective noise unavoidably non-Markovian. Thus, simulating a fault-tolerant circuit in this model does not automatically imply that there exists an accuracy threshold for the simulation similar to that applicable to the simulated fault-tolerant computation itself. Prior works have addressed the problem of obtaining such an accuracy threshold result by invoking a more general threshold theorem that holds for non-Markovian noise. Taking a different approach, we exploit the features of the fault-tolerant circuit design to show that this particular type of non-Markovian noise can in fact be handled by the standard accuracy threshold theorem.