3-Fermion topological quantum computation

TL;DR

This paper introduces a universal topological quantum computation scheme using 3-Fermion anyons, combining braiding, fusion, and magic state injection, with a fault-tolerant lattice implementation based on the Walker--Wang model.

Contribution

It develops a measurement-based topological quantum computing framework with thermally stable symmetry-protected order for the 3-Fermion anyon theory.

Findings

Provides a fault-tolerant lattice realization of the scheme

Demonstrates realization of symmetry defects in a 2D subsystem code

Establishes a connection between topological defects and code deformations

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.