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Abstract: We consider the possibility of adding noise to a quantum circuit to make itefficiently simulatable classically. In previous works this approach has beenused to derive upper bounds to fault tolerance thresholds - usually byidentifying a privileged resource, such as an entangling gate or a non-Cliffordoperation, and then deriving the noise levels required to make it`unprivileged-. In this work we consider extensions of this approach wherenoise is added to Clifford gates too, and then `commuted- around until itconcentrates on attacking the non-Clifford resource. While commuting noisearound is not always straightforward, we find that easy instances can beidentified in popular fault tolerance proposals, thereby enabling sharper upperbounds to be derived in these cases. For instance we find that if we takeKnill-s high threshold proposal together with the ability to prepare anypossible state in the $XY$ plane of the Bloch sphere, then no more than 3.69%error-per-gate noise is sufficient to make it classical, and 13.71% of Knill-sgamma noise model is sufficient. These bounds have been derived without noisebeing added to the decoding parts of the circuits. Introducing such noise in atoy example suggests that the present approach can be optimised further toyield tighter bounds.



Author: M. B. Plenio, S. Virmani

Source: https://arxiv.org/



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