Digital Simulation of Projective Non-Abelian Anyons with 68 Superconducting Qubits

Non-Abelian anyons are exotic quasiparticle excitations hosted by certain topological phases of matter.They break the fermion-boson dichotomy and obey non-Abelian braiding statistics:their interchanges yield unitary operations,rather than merely a phase factor,in a space spanned by topologically degenerate wavefunctions.They are the building blocks of topological quantum computing.However,experimental observation of non-Abelian anyons and their characterizing braiding statistics is notoriously challenging and has remained elusive hitherto,in spite of various theoretical proposals.Here,we report an experimental quantum digital simulation of projective non-Abelian anyons and their braiding statistics with up to 68 programmable superconducting qubits arranged on a two-dimensional lattice.By implementing the ground states of the toric-code model with twists through quantum circuits,we demonstrate that twists exchange electric and magnetic charges and behave as a particular type of non-Abelian anyons,i.e.,the Ising anyons.In particular,we show experimentally that these twists follow the fusion rules and non-Abelian braiding statistics of the Ising type,and can be explored to encode topological logical qubits.Furthermore,we demonstrate how to implement both single-and two-qubit logic gates through applying a sequence of elementary Pauli gates on the underlying physical qubits.Our results demonstrate a versatile quantum digital approach for simulating non-Abelian anyons,offering a new lens into the study of such peculiar quasiparticles.