Simulation And Measurenment Of Topological Order Based On Fibonacci Anyon

In recent years,the mathematical concept of topology has attracted wide attention in the field of physics,while the quantum computer based on the principles of quantum mechanics has developed rapidly in the near future.Quantum computation are popular because of the strong computing power,which is far beyond the ordinary classical computers.However,decoherence and noise are two main obstacles to the realization of universal quantum computers.In order to break this bottleneck.On the one hand,quantum error correction is proposed.On the other hand,topological quantum computation is also proposed as a coping strategy.Because of the whole topological property of the system,topological quantum computation has natural capability which can immune environment noise.So topological quantum computation is also regarded as one efficient way to realize quantum computation and has maximum tolerance.The topological order is a new kind of phase of the matter which surpasses the Landau symmetry breaking paradigm and has potential application in topological quantum computation.Observing topological order is extremely challenging in real physical systems,but quantum simulator as a special purpose quantum computing device provides a way to characterize topological order.It is generally believed that the topological order can be fully described by F-matrix and R-matrix,where the R-matrix has been confirmed to be directly experimentally measured,however whether the F-matrix can be directly measured is unknown.If F-matrix and R-matrix can be directly measured by experiments,then we say that the topological order can be directly measured.In this paper,we show how to use digital quantum simulator to simulate the doubled Fibonacci order which is described by the model of string net model and measure its F-matrix,at the same time,the recognition of three topological sequences on the model is completed.Based on the effective simulation of the F-matrix,we can further simulate the braiding operation and finally perform topological quantum computation through the braiding operation of anyons.