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Title: | Upper bounds on fault tolerance thresholds of noisy Clifford-based quantum computers |
Authors: | Plenio, MB Virmani, S |
Keywords: | Quantum circuit;Fault tolerance thresholds;Noise levels;Clifford-based quantum computers |
Issue Date: | 2010 |
Publisher: | IOP Publishing Ltd |
Citation: | New Journal of Physics, 12: Article no. 033012, 2010 |
Abstract: | We consider the possibility of adding noise to a quantum circuit to make it efficiently simulatable classically. In previous works, this approach has been used to derive upper bounds to fault tolerance thresholds—usually by identifying a privileged resource, such as an entangling gate or a non-Clifford operation, and then deriving the noise levels required to make it 'unprivileged'. In this work, we consider extensions of this approach where noise is added to Clifford gates too and then 'commuted' around until it concentrates on attacking the non-Clifford resource. While commuting noise around is not always straightforward, we find that easy instances can be identified in popular fault tolerance proposals, thereby enabling sharper upper bounds to be derived in these cases. For instance we find that if we take Knill's (2005 Nature 434 39) fault tolerance proposal together with the ability to prepare any possible state in the XY plane of the Bloch sphere, then not more than 3.69% error-per-gate noise is sufficient to make it classical, and 13.71% of Knill's γ noise model is sufficient. These bounds have been derived without noise being added to the decoding parts of the circuits. Introducing such noise in a toy example suggests that the present approach can be optimized further to yield tighter bounds. |
Description: | Copyright © 2010 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. |
URI: | http://iopscience.iop.org/1367-2630/12/3/033012/ http://bura.brunel.ac.uk/handle/2438/8919 |
DOI: | http://dx.doi.org/10.1088/1367-2630/12/3/033012 |
ISSN: | 1367-2630 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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