Engineering complex topological memories from simple Abelian models

Abstract

In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviours. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. So-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology.

15 pages, 3 figures. To appear in Annals of Physics

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Topological fault-tolerance in cluster state quantum computation
• Topological Computation without Braiding
• Superconducting Nanocircuits for Topologically Protected Qubits
• Entanglement and topological entropy of the toric code at finite temperature
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Demonstrating anyonic fractional statistics with a six-qubit quantum simulator
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Experimental determination of the Berry phase in a superconducting charge pump
• Simulations of quantum double models
• Qudit surface codes and gauge theory with finite cyclic groups
• Scaling law for topologically ordered systems at finite temperature
• Non-abelian statistics from an abelian model

Cited by in corpus (13)

• Quantum memories at finite temperature
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Breakdown of a perturbed Z_N topological phase
• Cellular-automaton decoders for topological quantum memories
• Decoding non-Abelian topological quantum memories
• Quantum memories and error correction
• A family of stabilizer codes for $D({\mathbb{Z}}_2)$ anyons and Majorana modes
• Entropic Barriers for Two-Dimensional Quantum Memories
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• Non-Abelian Fusion Rules from an Abelian System
• SU($N$) Toric Code and Nonabelian Anyons
• Fracton and topological order in the XY checkerboard toric code
• A witness for topological order and stable quantum memories in abelian anyonic systems