Simulations of quantum double models

Abstract

We demonstrate how to build a simulation of two dimensional physical theories describing topologically ordered systems whose excitations are in one to one correspondence with irreducible representations of a Hopf algebra, D(G), the quantum double of a finite group G. Our simulation uses a digital sequence of operations on a spin lattice to prepare a ground "vacuum" state and to create, braid and fuse anyonic excitations. The simulation works with or without the presence of a background Hamiltonian though only in the latter case is the system topologically protected. We describe a physical realization of a simulation of the simplest non-Abelian model, D(S_3), using trapped neutral atoms in a two dimensional optical lattice and provide a sequence of steps to perform universal quantum computation with anyons. The use of ancillary spin degrees of freedom figures prominently in our construction and provides a novel technique to prepare and probe these systems.

24 pages, 2 figures

References in corpus (14)

• Controlled exchange interaction between pairs of neutral atoms in an optical lattice
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Entanglement and topological entropy of the toric code at finite temperature
• Coherent Quantum Optical Control with Subwavelength Resolution
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Anyonic interferometry and protected memories in atomic spin lattices
• Creation and Manipulation of Anyons in the Kitaev Model
• Qudit surface codes and gauge theory with finite cyclic groups
• Addressing individual atoms in optical lattices with standing-wave driving fields
• The Non-Equilibrium Reliability of Quantum Memories
• Quantum Self-Correcting Stabilizer Codes
• Revealing anyonic features in a toric code quantum simulation
• Serial composition of quantum coin-flipping, and bounds on cheat detection for bit-commitment