3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators

Abstract

We describe a method for engineering local $k+1$-body interactions ($k=1,2,3$) from two-body couplings in spin-$12$ systems. When implemented in certain systems with a flat single-particle band with a unit Chern number, the resulting many-body ground states are fractional Chern insulators which exhibit abelian and non-abelian anyon excitations. The most complex of these, with $k=3$, has Fibonacci anyon excitations; our system is thus capable of universal topological quantum computation. We then demonstrate that an appropriately tuned circuit of qubits could faithfully replicate this model up to small corrections, and further, we describe the process by which one might create and manipulate non-abelian vortices in these circuits, allowing for direct control of the system's quantum information content.

4 pages + references and supplemental information

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• Realization of fractional quantum Hall state with interacting photons
• Passive correction of quantum logical errors in a driven, dissipative system: a blueprint for an analog quantum code fabric
• Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
• Elastic Multi-Body Interactions on a Lattice
• Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers
• Universal two-qubit interactions, measurement and cooling for quantum simulation and computing
• Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• Coherence of the Borromean three-body Förster resonances in Rydberg atoms
• Non-bosonic moiré excitons
• Continuous error correction for Ising anyons
• Stabilizing the Laughlin state of light: dynamics of hole fractionalization
• Effective models of doped quantum ladders of non-Abelian anyons
• Stability of Fractional Quantum Hall States in Disordered Photonic Systems