Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing
arXiv:2207.08928 · doi:10.3390/sym14091780
Abstract
We show that quasicrystals exhibit anyonic behavior that can be used for topological quantum computing. In particular, we study a correspondence between the fusion Hilbert spaces of the simplest non-abelian anyon, the Fibonacci anyons, and the tiling spaces of a class of quasicrystals, which includes the one dimensional Fibonacci chain and the two dimensional Penrose tiling. A possible encoding on tiling spaces of topological quantum information processing is also discussed.
References in corpus (31)
- Quantum Error Correction for Quantum Memories
- State preservation by repetitive error detection in a superconducting quantum circuit
- Fractional statistics in anyon collisions
- Interacting anyons in topological quantum liquids: The golden chain
- Quantum Low-Density Parity-Check Codes
- Epitaxy of Advanced Nanowire Quantum Devices
- Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential
- A short introduction to Fibonacci anyon models
- Topological phases without crystalline counterparts
- Complete Band Gaps in 2D Photonic Quasicrystals
- Observation of Edge Solitons in Photonic Graphene
- Photonic Floquet Topological Insulator in an Atomic Ensemble
- Critical eigenstates and their properties in one and two dimensional quasicrystals
- Topological models in rotationally symmetric quasicrystals
- Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
- Many-body localization in a quasiperiodic Fibonacci chain
- Topological states in quasicrystals
- Kohn-Luttinger mechanism driven exotic topological superconductivity on the Penrose lattice
- Quantum Computation Protocol for Dressed Spins in a Global Field
- Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
- Chern and Majorana Modes of Quasiperiodic Systems
- Topological Gaps by Twisting
- Effective Field Theory for Quasicrystals and Phasons Dynamics
- Confining massless Dirac particles in two-dimensional curved space
- Majorana Zero-Energy Mode and Fractal Structure in Fibonacci-Kitaev Chain
- Electrons in deterministic quasicrystalline potentials and hidden conserved quantities
- Brillouin zone labelling for quasicrystals
- A comparative study of universal quantum computing models: towards a physical unification
- Effect of coordination on topological phases on self-similar structures
- Character varieties and algebraic surfaces for the topology of quantum computing
- Tilings, tiling spaces and topology