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====== The Power of Noisy Fermionic Quantum Computation ======

Data: Sexta-Feira 05/07/2013 Sala A5-01, 11:00\\

Palestrante: Fernando Melo (CBPF)\\

Título: The Power of Noisy Fermionic Quantum Computation\\

Resumo: 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 [Phys. Rev. A 73, 042313 (2006)] that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular 4-fermion ancilla is below 40%. We show that above 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. On the other hand, 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 fermionic 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.
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Based on joint work with Piotr Cwiklinski, and Barbara M. Terhal. arXiv:1208.5334

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