Anyons are quasiparticles occurring in two dimensions, whose topological properties are believed to be robust against local perturbations and may hold promise for fault tolerant quantum computing. Here we present an experiment of demonstrating the path independent nature of anyonic braiding statistics with a superconducting quantum circuit, which represents a 7-qubit version of the toric code model. We dynamically create the ground state of the model, achieving a state fidelity of 0.688±0.015 as verified by quantum state tomography. Anyonic excitations and braiding operations are subsequently implemented with single-qubit rotations. The braiding robustness is witnessed by looping an anyonic excitation around another one along two distinct, but topologically equivalent paths: Both reveal the nontrivial π-phase shift, the hallmark of Abelian 1/2 anyons, with a phase accuracy of ∼99% in the Ramsey-type interference measurement.
Parafermions, which can be viewed as a fractionalized version of Majorana modes, exhibit profound non-Abelian statistics and emerge in topologically ordered systems, while their realization in experiment has been challenging. Here we propose a novel experimental scheme for the quantum simulation of parafermions and their non-Abelian braiding statistics in superconducting (SC) circuits by realizing the
Zd plaquette model on a two-dimensional lattice. Two protocols using quantum circuits and non-destructive measurements are introduced to prepare the topologically ordered ground state, on which parafermion pairs are created by engineering dislocations. We then propose a generalized code deformation approach to realize the fusion and non-Abelian braiding of parafermions, and show the application of this approach to the
Z3 parafermions. We also examine the real experimental parameter regime to confirm the feasibility of our scheme in SC devices. This work extends previous quantum simulations of topological defects in SC qubits to qudit systems and opens up a promising way for parafermion-based high-dimensional topological quantum computing with experimental feasibility.
The finding of physical realizations of topologically ordered states in experimental settings, from condensed matter to artificial quantum systems, has been the main challenge en route to utilizing their unconventional properties.We show how to realize a large class of topologically ordered states and simulate their quasiparticle excitations on a digital quantum computer.To achieve this, we design a set of linear-depth quantum circuits to generate ground states of general string-net models together with unitary open-string operators to simulate the creation and braiding of Abelian and non-Abelian anyons.We show that the Abelian (non-Abelian) unitary string operators can be implemented with a constant-(linear-) depth quantum circuit.Our scheme allows us to directly probe characteristic topological properties, including topological entanglement entropy, braiding statistics, and fusion channels of anyons.Moreover, this set of efficiently prepared topologically ordered states has potential applications in the development of fault-tolerant quantum computers.