3-Fermion topological quantum computation

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 Bombín -- making contact with an alternative implementation of the 3-Fermion defect computation scheme via code deformations.

31 pages, 34 figures, comments welcome, v2: published version

References in corpus (27)

• Generalized Global Symmetries
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
• Topological fault-tolerance in cluster state quantum computation
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Genons, twist defects, and projective non-Abelian braiding statistics
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Universal resources for measurement-based quantum computation
• Quantum computation on the edge of a symmetry-protected topological order
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Foliated Quantum Codes
• A magic state's fidelity can be superior to the operations that created it
• Pauli stabilizer models of twisted quantum doubles
• Logical blocks for fault-tolerant topological quantum computation
• Symmetry protection of measurement-based quantum computation in ground states
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Fault-tolerant qubit from a constant number of components
• Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
• Universal measurement-based quantum computation in two-dimensional SPT phases
• High-Fidelity Magic-State Preparation with a Biased-Noise Architecture
• Symmetry protected self correcting quantum memory in three space dimensions
• Universal resource-efficient topological measurement-based quantum computation via color-code-based cluster states
• Symmetry-protected adiabatic quantum transistors
• Invertible subalgebras

Cited by in corpus (7)

• Long-range entanglement from measuring symmetry-protected topological phases
• Anyon condensation and the color code
• XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
• Single-Shot Quantum Error Correction in Intertwined Toric Codes
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
• Condensation Completion and Defects in 2+1D Topological Orders
• Planar fault-tolerant circuits for non-Clifford gates on the 2D color code