QIP2021 | 3-Fermion topological quantum computation (Sam Roberts)

Authors: Sam Roberts and Dominic Williamson
Affiliations: PsiQuantum | Stanford University

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 Bombin -- pointing to an alternative implementation of our 3-Fermion defect computation scheme via code deformations.

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