3-Fermion Topological Quantum Computation

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 realization 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 two-dimensional subsystem code due to Bombín—making contact with an alternative implementation of the 3-fermion defect-computation scheme via code deformations.