Non-Abelian Anyons with Rydberg Atoms
arXiv:2301.04250 · doi:10.1103/PhysRevA.107.062407
Abstract
We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant quantum computing, have not been generated. To generate anyons with non-Abelian braiding statistics, we consider systems with mixed-boundary punctures. We obtain the topologically distinct ground states of the system numerically using the iDMRG technique. We discuss how these topological states can be created using ancilla atoms of a different type. We show that a system with 2N+2 punctures and an equal number of ancilla atoms leads to N logical qubits whose Hilbert space is determined by a set of stabilizing conditions on the ancilla atoms. Quantum gates can be implemented using a set of gates acting on the ancilla atoms that commute with the stabilizers and realize the braiding group of non-Abelian Ising anyons.
arXiv comment9 pages, 8 figures
References in corpus (26)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Anyons in an exactly solved model and beyond
- Surface codes: Towards practical large-scale quantum computation
- Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles
- Fast quantum gates for neutral atoms
- Observation of Rydberg blockade between two atoms
- Zoo of quantum-topological phases of matter
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- Observation of collective excitation of two individual atoms in the Rydberg blockade regime
- Entanglement of atoms via cold controlled collisions
- Quantum Logic Gates in Optical Lattices
- Direct observation of anyonic braiding statistics at the =1/3 fractional quantum Hall state
- Fractional statistics in anyon collisions
- Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
- Topological Order with a Twist: Ising Anyons from an Abelian Model
- Genons, twist defects, and projective non-Abelian braiding statistics
- Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins in the nuclear solid-state environment
- Prediction of Toric Code Topological Order from Rydberg Blockade
- Quantum phases of Rydberg atoms on a kagome lattice
- Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
- Poking holes and cutting corners to achieve Clifford gates with the surface code
- Fast Quantum State Control of a Single Trapped Neutral Atom
- Demonstrating non-Abelian statistics of Majorana fermions using twist defects
- Non-Abelian statistics with mixed-boundary punctures on the toric code
- A Hierarchy of Anyon Models Realised by Twists in Stacked Surface Codes