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arXiv · 2011.04693

3-Fermion topological quantum computation

Sam Roberts·Dominic J. Williamson
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Abstract

We present a scheme for universal topological quantum computation based on Clifford complete braiding and fusion of symmetry defects in the 3-Fermion anyon theory, supplemented with magic state injection. We formulate a fault-tolerant measurement-based realisation of this computational scheme on the lattice using ground states of the Walker--Wang model for the 3-Fermion anyon theory with symmetry defects. The Walker--Wang measurement-based topological quantum computation paradigm that we introduce provides a general construction of computational resource states with thermally stable symmetry-protected topological order. We also demonstrate how symmetry defects of the 3-Fermion anyon theory can be realized in a 2D subsystem code due to Bomb\'{i}n -- making contact with an alternative implementation of the 3-Fermion defect computation scheme via code deformations.

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Sam Roberts, Dominic J. Williamson. 2020-11-09. 3-Fermion topological quantum computation. https://doi.org/10.1103/prxquantum.5.010315

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