Quantum Error Correction for Complex and Majorana Fermion Qubits
Mesoscale and Nanoscale Physics
2017-03-03 v1 Quantum Physics
Abstract
We introduce error-correcting codes that can correct for fermion parity-violating (quasiparticle poisoning) and parity-conserving errors in systems of complex fermions and of Majorana fermions. After establishing properties of fermion codes, we introduce a generic construction of fermion codes from weakly self-dual classical, binary error-correcting codes. We use this method to construct (i) the shortest fermion code to correct for quasiparticle poisoning errors, (ii) translationally-invariant fermion codes and (iii) other codes that correct higher-weight errors. We conclude by discussing a possible physical realizations of one such code in mesoscopic superconductors hosting Majorana zero modes.
Keywords
Cite
@article{arxiv.1703.00459,
title = {Quantum Error Correction for Complex and Majorana Fermion Qubits},
author = {Sagar Vijay and Liang Fu},
journal= {arXiv preprint arXiv:1703.00459},
year = {2017}
}
Comments
11 pages, 2 figures