期刊
NEW JOURNAL OF PHYSICS
卷 15, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/15/1/013015
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资金
- Vidi grant from the Netherlands Organization for Scientific Research (NWO) [639.072.803]
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.
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