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Is there a proof that measurement-based quantum computation can be fault tolerant under any noise model? Or at least, under any noise model with small enough correlation length?

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  • $\begingroup$ Is there a reason why the RHG paper doesn't meet this requirement? arxiv.org/abs/quant-ph/0510135 $\endgroup$ Jan 19, 2023 at 21:50
  • $\begingroup$ Yes- they consider relatively simple noise model, with only single-qubit, spacial and temporal independent errors (which can propagate to only a limited distance due to the preparation process). This is not the case in some realistic applications. $\endgroup$ Jan 22, 2023 at 10:31
  • $\begingroup$ For what it's worth, the RHG cluster state can correct arbitrary local errors, including loss. The errors don't have to be depolarizing or single-qubit $\endgroup$ Jan 22, 2023 at 20:23

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In "Fault-tolerant quantum computation with cluster states"[1], Nielsen and Dawson (2005) studied fault-tolerance in MBQC with cluster states. They proved threshold theorems similar to the well-known threshold theorem for quantum circuit model.

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  • $\begingroup$ Thanks. Do you know about a further work that generalize their work to include both leakage/loss and non-Markovian noise, or that uses weaker noise locality assumptions? $\endgroup$ Jan 22, 2023 at 10:33

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