The power of noisy fermionic quantum computation

Fernando De Melo*, Piotr Ćwikliński, Barbara M. Terhal

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

24 Citations (Scopus)


We consider the realization of universal quantum computation through braiding of Majorana fermions supplemented by unprotected preparation of noisy ancillae. It has been shown by Bravyi (2006 Phys. Rev. A 73 042313) that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular four-fermion ancilla is below 40%. We show that beyond a noise rate of 89% on this ancilla the quantum computation can be efficiently simulated classically: we explicitly show that the noisy ancilla is a convex mixture of Gaussian fermionic states in this region, while for noise rates below 53% we prove that the state is not a mixture of Gaussian states. These results are obtained by generalizing concepts in entanglement theory to the setting of Gaussian states and their convex mixtures. In particular, we develop a complete set of criteria, namely the existence of a Gaussian-symmetric extension, which determine whether a state is a convex mixture of Gaussian states.

Original languageEnglish
Article number013015
Number of pages21
JournalNew Journal of Physics
Publication statusPublished - 2013
Externally publishedYes


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